We introduce a novel focus shaping concept for intrastromal corneal dissection that facilitates cleavage along corneal lamellae, and we analyze laser-tissue interactions governing cutting effectiveness and mechanical side effects. Methods: Focus shaping was achieved by a spiral phase plate that converts an incident Gaussian beam into a Laguerre-Gaussian beam with a helical phase. Such vortex beams have zero intensity at their center, are propagation invariant, and possess a ring focus equal in length to the Gaussian focus but with a larger diameter. Cutting precision and the required absorbed energy for flap dissection were compared for Gaussian and vortex beams on ex vivo porcine corneal specimens at pulse durations between 480 fs and 9 ps. Cutting quality and bubble formation were characterized by scanning electron microscopy and macro photography. Results: With the vortex beam, the cuts were much smoother. Bubble formation was markedly reduced because cutting can be performed close to the bubble threshold, whereas with the Gaussian beam energies well above threshold are needed. Although the incident energy at the flap dissection threshold was slightly larger for the vortex beam, the absorbed energy was much smaller and contributed more effectively to cutting. This reduced plasma-induced pressure more than sevenfold. Conclusions: The vortex beam approach for corneal dissection is a simple, versatile, and cost-effective way of improving the precision of refractive surgery while reducing bubble formation and pressure-related mechanical side effects. Translational Relevance: Phase plates for propagation invariant vortex beams are easily implemented in the beam path of next-generation clinical devices.