NO diagram program in the entire world does; the MS format is private, undocumented, and darn hard to crack -- Omnigraffle will open Visio files if they were saved as .XML -- same for the app ConceptDraw -- the only problem is that PC users save their Visio files as .vsd -- so the short answer is: there is NO Mac program that opens .vsd files directly.
Actually, I use OmniGraffle Pro 5 to open vsd files. The fidelity of the import varies depending on the drawing; sometimes lines and text blocks get screwed up, but never anything major. OG exports to .vdx, and again, sometimes you'll need to tweak things in Visio.