Isaiah in rabbinic literature
Baraita of Rabbi Ishmael
—— Tannaitic ——
Isaiah chosen as a prophet 
While Isaiah, says the Midrash, was walking up and down in his study he heard God saying, "Whom shall I send ?" Then Isaiah said, "Here am I; send me!" Thereupon God said to him," My children are trouble-some and sensitive; if thou art ready to be insulted and even beaten by them, thou mayest accept My message; if not, thou wouldst better renounce it" (Lev. R. x.). Isaiah accepted the mission, and was the most forbearing, as well as the most ardent patriot, among the Prophets, always defending Israel and imploring forgiveness for its sins. When Isaiah said, "I dwell in the midst of a people of unclean lips" Isaiah 6:5 he was rebuked by God for speaking in such terms of His people (Canticles Rabbah 1.6).
Death of Isaiah 
It is related in the Talmud that Rabbi Simeon ben Azzai found in Jerusalem an account wherein it was written that King Manasseh killed Isaiah. King Manasseh said to Isaiah, "Moses, thy master, said, 'There shall no man see God and live' Exodus 33:20; but thou hast said, 'I saw the Lord seated upon his throne'" Isaiah 6:1; and went on to point out other contradictions—as between Deuteronomy 4:7 and Isaiah 40:6; between Exodus 33:26 and 2 Kings 20:6. Isaiah thought: "I know that he will not accept my explanations; why should I increase his guilt?" He then uttered the Unpronounceable Name, a cedar-tree opened, and Isaiah disappeared within it. Then King Manasseh ordered the cedar to be sawn asunder, and when the saw reached his mouth Isaiah died; thus was he punished for having said, "I dwell in the midst of a people of unclean lips" (Yeb. 49b).
A somewhat different version of this legend is given in the Jerusalem Talmud (Sanhedrin x.). According to that version Isaiah, fearing King Manasseh, hid himself in a cedar-tree, but his presence was betrayed by the fringes of his garment, and King Manasseh caused the tree to be sawn in half. A passage of the Targum to Isaiah quoted by Jolowicz ("Die Himmelfahrt und Vision des Prophets Jesajas," p. 8) states that when Isaiah fled from his pursuers and took refuge in the tree, and the tree was sawn in half, the prophet's blood spurted forth. From Talmudical circles the legend of Isaiah's martyrdom was transmitted to the Arabs ("Ta'rikh," ed. De Goeje, i. 644).