A sheet processing apparatus which is capable of improving the productivity of sheet processing as much as possible. An image forming apparatus forms an image on a sheet. A finisher is connected downstream of the image forming apparatus and performs post processing on the sheet. The finisher moves at least one of the sheet and a punching unit to adjust a position for punching holes in the sheet. The finisher determines whether or not a post-processing apparatus connected upstream of the finisher is provided with a correction mechanism for correcting a position of a sheet in a direction orthogonal to a sheet conveying direction. When the post-processing apparatus is provided with the correction mechanism, the finisher causes the image forming apparatus to be set such that a sheet conveying interval becomes shorter than when the post-processing apparatus is not provided with the correction mechanism.