In this paper, the tracking control of an automatic pipe cutting robot, called APCROM, with a magnetic binder is studied. Using magnetic force APCROM, a wheeled robot, binds itself to the pipe and executes unmanned cutting process. The gravity effect on the movement of APCROM varies as it rotates around the pipe laid in the gravitational field. In addition to the varying gravity effect other types of nonlinear disturbances including backlash in the driving system and the slip between the wheels of APCROM and the pipe also cause degradation in the cutting process. To maintain a constant velocity and consistent cutting performance, the authors adopt a repetitive learning controller (MRLC), which learns the required effort to cancel the tracking errors. An angular-position estimation method based on the MEMS-type accelerometer is also used in conjunction with MRLC to compensate the tracking error caused by slip at the wheels. Experimental results verify the effectiveness of the proposed control scheme.