A surgical stapler for stapling the tissue of a patient, comprising: a handle; a shaft extending from said handle; an end effector comprising a distal head and an end effector axis, comprising: a tissue compression surface; and an anvil comprising staple forming pockets, wherein said anvil is movable toward said tissue compression surface during a closing motion; wherein the end effector is configured to accept a staple cartridge including a plurality of staples removably stored therein; a motorized drive system comprising a rotatable drive shaft; an anvil closing system configured to move said anvil through said closing motion, wherein said anvil closing system is coupled to and operable by said rotatable drive shaft; a firing system configured to deploy said staples along a firing path; and a propulsion system configured to move said end effector relative to the patient tissue during a propulsion motion, wherein said propulsion system is coupled to and operable by said rotatable drive shaft, and wherein said propulsion motion is transverse to said closing motion; wherein the propulsion system is a tissue drive system (1380a, 1380b) with the tissue compression surface defined on the tissue drive system (1380a, 1380b); and wherein the tissue drive system (1380a, 1380b) is configured to engage the patient tissue and move the surgical stapler relative to the patient tissue to thereby reposition the distal head along said firing path, characterized in that: said closing motion is along said end effector axis, and said propulsion motion is transverse to said end effector axis. a handle; a shaft extending from said handle; an end effector comprising a distal head and an end effector axis, comprising: a tissue compression surface; and an anvil comprising staple forming pockets, wherein said anvil is movable toward said tissue compression surface during a closing motion; a tissue compression surface; and an anvil comprising staple forming pockets, wherein said anvil is movable toward said tissue compression surface during a closing motion; wherein the end effector is configured to accept a staple cartridge including a plurality of staples removably stored therein; a motorized drive system comprising a rotatable drive shaft; an anvil closing system configured to move said anvil through said closing motion, wherein said anvil closing system is coupled to and operable by said rotatable drive shaft; a firing system configured to deploy said staples along a firing path; and a propulsion system configured to move said end effector relative to the patient tissue during a propulsion motion, wherein said propulsion system is coupled to and operable by said rotatable drive shaft, and wherein said propulsion motion is transverse to said closing motion; wherein the propulsion system is a tissue drive system (1380a, 1380b) with the tissue compression surface defined on the tissue drive system (1380a, 1380b); and wherein the tissue drive system (1380a, 1380b) is configured to engage the patient tissue and move the surgical stapler relative to the patient tissue to thereby reposition the distal head along said firing path, characterized in that: said closing motion is along said end effector axis, and said propulsion motion is transverse to said end effector axis.