This psalm, like the two previous psalms, is ascribed to Asaph (see Introduction to Ps. 73), and there is no reason to doubt that it is correctly attributed to him. On the phrase in the title, "To the chief Musician," see Introduction to Psalm 4:1-8. On the phrase "Al-taschith," see the notes on the title to Psalm 57:1-11. The phrase "A Psalm or Song" (in Hebrew, "a psalm - a song"), occurs also in the title, to other psalms, as Psalm 30:1-12; Psalm 65:1-13, etc.
It is not possible now to determine the occasion on which this psalm was composed, as it is not indicated in the title, and there are no historical references in the psalm itself which would enable us to ascertain it. The general purpose is indicated in Psalm 75:1, which is to ascribe praise to God for some particular manifestation of his favor. So far as can be conjectured from the psalm, there are two things which may have been referred to.
(I) The first is, that it was composed by someone - or for some one, in his name, as expressing his feelings - who was about to enter on the administration of the affairs of the nation, apparently a young prince soon to ascend the throne. See Psalm 75:2, "When I shall receive the congregation," etc.
(II) The second is, that it would seem to have been a time of national danger; a time when there may have been other aspirants for the throne; a time when wicked and powerful men had combined for the purpose of usurping the authority, and setting aside the legitimate claimant to power, or when there seemed to have been a universal dissolution of authority, or general anarchy. See Psalm 75:3, "The earth and all the inhabitants thereof are dissolved." Compare Psalm 75:4-5.
In these circumstances, in this general rebellion, in this time of resistance to lawful authority, and of combination and conspiracy against right, the speaker in the psalm expresses confidence in God as the source of all authority Psalm 75:6; as the "Judge" Psalm 75:7; as a God in whose hand is a cup of punishment which he will administer to all wicked people, Psalm 75:8. "The psalm, therefore, expresses confidence in God in the endeavor to assert the claims of legitimate authority."
Another, and a more common view, however, has been taken of the psalm, which is, that it refers to God as the Ruler among the nations, and as asserting that he will in due time take vengeance on those who are in rebellion against him. This is the view of DeWette, Prof. Alexander, Luther, and others. It was also the view taken by the translators of the Septuagint, and the Latin Vulgate. Compare, however, the notes at Psalm 75:2.
The contents of the psalm are as follows:
(1) A purpose of the author of the psalm to praise God for the manifestation of his wondrous works, Psalm 75:1.
(2) his purpose when he should "receive the congregation," or should be invested with authority, to judge uprightly, or to discharge his duties with fidelity, Psalm 75:2.
(3) a statement of the existing disorder and confusion, as if the very structure of society was broken up, Psalm 75:3.
(4) advice addressed to the authors of the prevailing disorder not to pursue their plans of evil Psalm 75:4-8, for two reasons:
(a) Promotion or success must come from God, or from his counsels, and not by chance, or by any laws of nature Psalm 75:6-7; and
(b) because God is a righteous Judge, and the wicked can expect nothing but punishment at his hand, Psalm 75:8.
(5) a purpose to praise God, in view of the fact that all the power of the wicked would be broken, but the power of the righteous would be maintained and exalted, Psalm 75:9-10.

The psalmist praises God for present mercies, Psalm 75:1; the Lord answers, and promises to judge the people righteously, Psalm 75:2, Psalm 75:3; rebukes the proud and haughty, Psalm 75:4, Psalm 75:5; shows that all authority comes from himself, Psalm 75:4-7; that he will punish the wicked, Psalm 75:8; the psalmist resolves to praise God, Psalm 75:9; and the Most High promises to cast down the wicked, and raise up the righteous, Psalm 75:9, Psalm 75:10.
The title is, "To the chief Musician, or conqueror, Al-taschith, destroy not, A Psalm or Song of Asaph." See this title Al-taschith explained Psalm 57:1-11 : The Chaldee supposes that this Psalm was composed at the time of the pestilence, when David prayed the Lord not to destroy the people. Some of the Jews suppose that Al-taschith is the beginning of a Psalm, to the air of which this Psalm was to be set and sung. The Psalm seems to have been composed during the captivity; and appears to be a continuation of the subject in the preceding.

INTRODUCTION TO PSALM 75
To the chief Musician, Altaschith, A Psalm or Song of Asaph. Of the word "altaschith", See Gill on Psalm 57:1, it signifies "do not destroy", or "do not corrupt"; the Targum renders it,
"do not destroy thy people;''
so Jarchi,
"do not destroy Israel;''
perhaps it may be considered as a petition, that God would not suffer the man of sin to go on to destroy the earth, and corrupt the inhabitants of it with his false doctrine, idolatry, and superstition, Revelation 11:18, for the psalm respects the times of the Gospel dispensation, and includes both the first coming of Christ in the flesh, and his second coming to judgment; the argument of it with the Syriac version is,
"the divinity of Christ, and a remembrance of the judgment;''
it is said to be a psalm or song of Asaph, but is thought to be written by David, and delivered to Asaph; for it may be rendered "for Asaph" (k); and so the Targum,
"by the hands of Asaph;''
though some think it was written after the Babylonish captivity; perhaps by some person whose name was Asaph, or was of the family of him that lived in David's time. Theodoret supposes it was written in the person of the captives in Babylon.

(Psalm 75:1-5) The psalmist declares his resolution of executing judgment.
(Psalm 75:6-10) He rebukes the wicked, and concludes with resolutions to praise God.

The Nearness of the Judge with the Cup of Wrath
That for which Ps 74 prays: Arise, Jahve, plead Thine own cause (Psalm 74:22.), Psalm 75:1-10 beholds; the judgment of God upon the proud sinners becomes a source of praise and of a triumphant spirit to the psalmist. The prophetic picture stands upon a lyrical groundwork of gold; it emerges out of the depth of feeling, and it is drawn back again into it. The inscription: To the Precentor, (after the measure:) Destroy not (vid., on Psalm 57:1), a Psalm by Asaph, a Song, is fully borne out. The Sela shows that the Psalm, as מזמור שׁיר says, is appointed to be sung with musical accompaniment; and to the לאסף corresponds its thoroughly Asaphic character, which calls Ps 50 to mind with especial force. But from this Psalm Psalm 75:1-10 differs, however, in this particular, viz., that a more clearly defined situation of affairs manifests itself through the hope of the judicial interposition of God which is expressed in it with prophetic certainty. According to appearances it is the time of the judgment of the nations in the person of Assyria; not, however, the time immediately following the great catastrophe, but prior to this, when Isaiah's prophecy concerning the shattering of the Assyrian power against Jerusalem had gone forth, just as Hengstenberg also regards this Psalm as the lyrical companion of the prophecies which Isaiah uttered in the presence of the ruin which threatened from Assyria, and as a testimony to the living faith with which the church at that time received the word of God. Hitzig, however, assigns both Psalm 75:1-10 and Psalm 76:1-12 to Judas Maccabaeus, who celebrates the victory over Apollonius in the one, and the victory over Seron in the other: "we may imagine that he utters the words of Ps 75:11 whilst he brandishes the captured sword of the fallen Apollonius." But the probability that it refers to the Assyrian period is at least equally balanced with the probability that it refers to the Maccabaean (vid., Psalm 75:7; Psalm 76:5-7); and if the time of Hezekiah were to be given up, then we might sooner go back to the time of Jehoshaphat, for both songs are too original to appear as echoes and not much rather as models of the later prophecy. The only influence that is noticeable in Psalm 75:1-10 is that of the Song of Hannah.