Generation of vortex beams directly from the laser source can be limited in power and efficiency, or to specific pump sources and gain media. Here, we propose a new high power and high efficiency vortex laser methodology with interferometric mode transformation as output coupling, which uses high power handling and low loss optics that have wavelength versatility. Experimental demonstration is made in a diode-pumped Nd:YVO4 laser using an imbalanced Sagnac interferometer as output coupler producing high quality vortex output beams (M2 = 2.07) with fully selectable control of handedness whilst the intracavity mode is maintained as a fundamental Gaussian. Vortex output power >3W is produced with only small reduction in efficiency compared to the equivalent TEM00 laser. Continuous variation of vortex output coupling transmission and the quality of the vortex is investigated experimentally showing good agreement with theory. This work reveals a new approach to high power structured laser radiation direct from the source through interferometric spatial mode transformations.