A rotating control device can include a housing assembly, a body and a clamp device which releasably secures the housing assembly to the body. The clamp device can include a piston which radially displaces a clamp section. A well system can include a rotating control device which includes at least one seal which seals off an annulus between a body of the rotating control device and a tubular string which extends longitudinally through the rotating control device. The rotating control device can also include a piston which displaces longitudinally and selectively clamps and unclamps a housing assembly to the body.