To provide a sheet processing apparatus capable of preventing cutting waste from adhering to a fixed blade, and to provide an image forming apparatus.

The sheet processing apparatus has a liftable/lowerable upper blade 633 and a lower blade 634, which cuts a sheet bundle placed between the lower blade 634 and the upper blade 633 by making the upper blade 633 come down. Then, by a linkage component comprising a rotary cam 690, link 637a, and arm 6740, a scraping sheet 692 is lowered interlocked with the lowering of the upper blade 633 so that cut parts of the cut sheet bundle can fall without adhering to the lower blade 634.