Why would it scatter, precisely? As long as the beam remained at the center of the prism face (on whichever side is being fed the beam), and there are no major imperfections in the prism to reflect/refract light in the wrong direction, it should be fine...right? Not unlike how a parascope can function 360 degrees without distorting the images.
Unless I'm mistaken, so long as the prism, the beam itself, and beam's entry position isn't asymmetrical, rotating a reflective prism should be an issue. Even firing at a depression or higher angle shouldn't be an issue so long as the prism has a symmetrical surface (keep in mind "prism" isn't merely limited to triangular. There are half-circle prisms, Amici roof prisms, pentaprims, etc).
As to how it would survive: Reinforcing a very small point of a vessel, such as a prism, would be I imagine a trivial task. By standard engineering practices, small amounts of armor can be reinforced by a significant factor in laboratories settings by using support systems that are usually to troublesome, bulky, or expensive to mass produce. i.e., giant shock absorbers on tank armor, prohibitively expensive materials that can't be used in mass production, etc.
To make a single object withstand a high intensity beam should be relatively simple matter, as the prism's integrity can be increased theoretically with the appropriate additions; quality materials, high-efficiency thermal sinks to draw heat quickly from the prism, multiple active cooling systems, forcefield assisted protective, and so on.