road bike to road bike with mountain bike fram with full suspension
Adding rear suspension to an existing bike not designed for rear suspension is hard - you'd have to cut the tubes, weld them and make sure the result is safe.

Adding front suspension to a bike is not so hard, but it will change the geometry. You need to find the specs of the fork and headset that are in the bike already, and then find something compatible (threadless/threaded, steerer tube diameter). However, adding a front suspension to a bike which wasn't really designed for it is not necessarily advisable -- the rest of it may not hold up to the abuse you may be thinking of giving the bike after you put on a fork.

As pointed out in DWGKNZ's answer, you can't swap a lot of the parts (the Specialized Demo 8 uses pressfit BB, so you'll get a new crank at the minimum), but given the tools required and the fact that the sirrus comp is a nice bike, you're better off selling it and buying new parts. On top of that, the parts for mountain biking (e.g. derailleurs, etc.) are built more robustly for mountain biking than for the road so you'd likely want to buy better parts anyway (esp. for a nice frame like a Demo 8).