The segmented large millimeter telescope (LMT/GTM) is the largest spatial light modulator capable of producing vortex beams of integer topological charge. This observing mode could be applied for direct exoplanet searches in the millimeter or submillimeter regimes. The stability of the vortex structure against aberrations and diffraction effects inherent to the size and segmented nature of the collector mirror was studied. In the presence of low-order aberrations, the focal distribution of the system remains stable. Results show that these effects depend on the topological charge of the vortex and the relative orientation of the aberration with respect to the antenna axis. Coma and defocus show no large effects in the image at the focal plane; however, the system is very sensitive to astigmatism. Heat turbulence, simulated by random aberrations, shows that the system behaves in a similar way as astigmatism dissociating the vortices. The segmented vortex telescope is proposed as a novel approach for the detection of giant planets outside circumstellar disks around nearby stars. Since results are applicable to other facilities with segmented surfaces, it is suggested that this idea should be considered as a regular observation mode complementary to interferometric methods.