put or go on the block. Offer for sale, as in These paintings will all be put on the block. This usage alludes to the auction block, the platform from which the auctioneer sells, so called since the mid-1800s.
put one's head on the block. Take a great risk, make oneself vulnerable, as in I'm not going to put my head on the block just to save her reputation. This usage alludes to the executioner's block, on which victims are beheaded, so called since the mid-1500s.