A tiltable anvil assembly is provided that includes an anvil head assembly that is tiltable from an operative position to a post-fired tilted position after firing of a circular stapler to minimize the profile of the anvil head assembly during removal of the anvil head assembly from a body lumen of a patient. In order to simplify removal of a tissue doughnut from the anvil head assembly after firing, the anvil assembly includes locking structure to retain the anvil head assembly in a post-fired doughnut removal position.