I just came across the word “mandamused” in a court opinion, so I did a couple of Westlaw searches — “mandamused” yields 238 hits, going back to the 1880s, and “mandamusing” yields 35 hits. The Oxford English Dictionary gives the first attestation as 1823 (and not even in a court case), though the sentence is a bit opaque, and possibly facetious: “If I do not ferk you out of all likelihood of ringing the beauty, why mandamus me!” (I kid you not.)
“Mandamus” is well-known to lawyers, and it means (to quote Black’s Law Dictionary) “A writ issued by a superior court to compel a lower court or a government officer to perform mandatory or purely ministerial duties correctly.” The verb form “to mandamus X” thus naturally means “to issue a writ of mandamus ordering X to do something”; this stems from a normal process of English word formation, but I just hadn’t myself seen this before. “Mandamusing” strikes me as a little funky-looking, perhaps because it reminds someone of “musing,” though I take it that this reaction would become less common if the word becomes more common. (Naturally, I’m talking here about how common the term is among lawyers; even the much more common noun is in practice technical jargon used in a technical context.)
As usual with relatively rare terms such as this — which might distract or annoy even if they don’t confuse — I would generally advise people to stay away from the verb “mandamus” unless they’re confident that it’s familiar to their audience (say, to the court of appeals). But judges of course have more flexibility.