Then the Jews again took up stones. As true religion, in maintaining the glory of God, burns with its own zeal which the Spirit of God directs, so unbelief is the mother of rage, and the devil hurries on the wicked in such a manner, that they breathe nothing but slaughter. This result shows with what intention they put the question to Christ; for the open confession, of which they pretended to be desirous, instantly drives them to madness. And yet, though they are hurried along, with such violence, to oppress Christ, there can be no doubt that they assigned some plausible reason for their judgment, as if they were acting according to the injunction of the Law, by which God commands that false prophets shall be stoned, (Deuteronomy 13:5.)

The Jews took up stones - Stoning was the punishment of a blasphemer, Leviticus 24:14-16. They considered him guilty of blasphemy because he made himself equal with God, John 10:33.
Again - They had before plotted against his life John 5:16, John 5:18, and once at least they had taken up stones to destroy him, John 8:59.

The Jews took up stones - To stone him as a blasphemer, Leviticus 24:14-16, because he said he was one with God. The evangelist adds the word again, because they had attempted to do this before, see John 8:59; but it seems they were prevented from doing this now by the following discourse.

(10) Then the Jews took up stones again to stone him.
(10) Christ proves his dignity by divine works.

Then the Jews took up stones again to stone him. As they had done before; see Gill on John 8:59;

Christ's works of power and mercy proclaim him to be over all, God blessed for evermore, that all may know and believe He is in the Father, and the Father in Him. Whom the Father sends, he sanctifies. The holy God will reward, and therefore will employ, none but such as he makes holy. The Father was in the Son, so that by Divine power he wrought his miracles; the Son was so in the Father, that he knew the whole of His mind. This we cannot by searching find out to perfection, but we may know and believe these declarations of Christ.

Then the Jews took up stones again to stone Him--and for precisely the same thing as before (John 8:58-59).