Hydraulic clamps are very common, both on heavier work where more clamping force is required, as well as on compact work where there isn't enough room for an air cylinder with sufficient force. Air over hydraulic intensifiers are often used to allow a pneumatic supply to operate a hydraulic clamp.
The commercial CNC controls pretty much all have some general purpose output signals available controlled by M functions to control clamping, signal indexers, palette changers, robots, etc. Really very easy stuff to do, and just as easy to do on home machines if you have a run of parts big enough to justify the fixturing.
If you search on McMaster for "clamping cylinder" you should find pneumatic and hydraulic cylinders intended for work clamping use. Even some tiny hydraulic clamp cylinders that have threaded bodies to install like a bolt.