We report on direct generation of an orthogonally polarized dual-wavelength vortex laser, for the first time to our knowledge, by means of a diode-pumped V-shaped Pr:YLF laser platform. A method of misaligning the folded mirror is proposed to realize the simultaneous orthogonally polarized dual-wavelength laser, while a method of orthogonally rotating the laser gain medium is proposed to generate an intracavity vortex beam (LG01 mode). With the two methods, in continuous-wave (CW) mode, we have achieved simultaneous lasing of an orthogonally polarized dual-wavelength vortex laser at 604 and 607nm with maximum output power of 237.7mW. Moreover, based on this operation, a simultaneous orthogonally polarized dual-wavelength passively Q-switched vortex laser is also realized by inserting a Co:ASL crystal into the laser resonator as a saturable absorber. This work provides the simplest way for direct generation of an orthogonally polarized dual-wavelength vortex laser for potential applications.