A machine for cutting or beveling a pipe. A cutter unit rotates around the pipe while cutting any surface of the pipe after gripping and fixing the pipe. The machine includes: a main body which a pipe passes through the center portion thereof to be fixed; and a cutter unit coupled to the main body unit rotates around the fixed pipe to cut or bevel the pipe. The cutter unit may have a rotating unit on one side to pull the cutter unit aside and a locking unit on the other side to restrain or release the cutter unit. An entry control unit operating the cutter unit includes: a lever gear-engaged with an outer side surface of an entry control plate; and a clutch formed on a rotation shaft of the lever such that the restraint is released when the lever is lifted or pressed in the axial direction.