In a conventional gyrotron with a cylindrical cavity, the nonsymmetric modes rotate azimuthally, forming two orthogonal vortex waves with different rotating directions. However, such two waves can be degenerated due to the effect of a misaligned electron beam. The paper investigates the degeneracy and mode competition of two oppositely rotating modes in an THz gyrotron with a misaligned electron beam, using a multimode, time-dependent, self-consistent model. The results show that the beam misalignment induces azimuthal nonuniformity of beam-wave coupling strength, which can lead to the cooperative existence of two oppositely rotating modes. This provides insights into understanding the experimental results where quasi-standing-wave patterns is observed in a THz gyrotron.