The copper mold of the micro-triangular pyramid (MTP) is a key component of MTP plastic film manufacturing, and its optical functional surface comprises micro-triangular pyramid arrays (MTPAs). The edge burrs of MTPAs severely affect the optical properties of MTP plastic film. To solve the problem of excessive edge burr of MTPA machining using the fly-cutting method, the orthogonal experimental method was used to optimize the four influencing factors: fly-cutting speed, feed speed, cutting depth, and cooling mode. The results show that the impact of these influencing factors on surface roughness, the projected area of the exit edge burr, and exit edge burr thickness are ranked from largest to the smallest as follows: fly-cutting speed, feed speed, cutting depth, and cooling mode. The factors affecting tool nose wear in descending order are fly-cutting speed, feed speed, cooling mode, and cutting depth. The optimal conditions for minimizing the thickness of the edge burr were a fly-cutting speed of 7.85 m/s, a feed speed of 50 mm/min, a finishing cutting depth of 15 μm, and using compressed air with oil mist for cooling. This study lays a foundation for improving the anti-reflection performance of MTP plastic film.