Dissipative nonlinear wave dynamics have been investigated extensively in mode-locked lasers with single transverse mode, whereas there are few studies related to three-dimensional nonlinear dynamics within lasers. Recently, spatiotemporal mode locking (STML) was proposed in lasers with small modal (i.e., transverse-mode) dispersion, which has been considered to be critical for achieving STML in those cavities because the small dispersion can be easily balanced. Here, we demonstrate that STML can also be achieved in multimode lasers with much larger modal dispersion, where we find that the intracavity saturable absorber plays an important role for counteracting the large modal dispersion. Furthermore, we observe a new STML phenomenon of passive nonlinear autoselection of single-mode mode locking, resulting from the interaction between spatiotemporal saturable absorption and spatial gain competition. Our work significantly broadens the design possibilities for useful STML lasers thus making them much more accessible for applications, and extends the explorable parameter space of the novel dissipative spatiotemporal nonlinear dynamics that can be achieved in these lasers.