The phrase “to sweat blood” means to perform such arduous toil or to be in such physical agony that the sweat in which one is bathed seems to be one’s blood draining away.
The allusion is to the agony of Jesus on the Mount of Olives: “And being in an agony he prayed more earnestly: and his sweat was as it were great drops of blood falling down to the ground.”
The expression had only a religious use until about the seventeenth century.