Carbon fiber reinforced polymer (CFRP) composites are widely used in the aerospace field because of their outstanding performance. Laser is an effective method for CFRP composite processing. However, there are corner errors and obvious thermal damage in laser corner cutting, which affect the cutting quality. This article mainly describes the corner error and thermal damage behavior, and the effect of anisotropy of nanosecond UV laser when cutting different corners of CFRP plates. Select six corner angles to perform a full factorial experiment with a right-angled triangle hole cutting under the horizontal and vertical baselines and different laser repetition rates. The results show that there are obvious corner errors and heat affected zone (HAZ) and matrix recession (MR) in laser corner cutting. The corner error always shows that the cut-in error is smaller than the cut-out error (28.06% on average), and the cut-in error and HAZ decrease with the increase of the corner angle, but the difference between the cut-in and the cut-out error increases with the increase of the corner angle. In vertical baseline cutting, the corner error can be reduced to a certain extent, but the HAZ (average 38.42%) is seriously increased, and the thermal damage of linear cutting under a large pulse repetition rate is increased. The large laser repetition rate increases the thermal damage due to the increase of the overlap rate of adjacent pulses but has less effect on the corner error, especially the cut-in error.