I currently own a specialized sirrus comp, and I was wondering if I could swap all the parts on that bike other than the frame to a demo 8 frame with 200mm of travel. If it is possible to add full suspension to my road bike, that would be prefered.
Apart from these being very different frames with very different uses you won't have much luck transferring parts.
In terms of your bike there is very little that would fit:
Wheels - won't fit - the demo 8 has a 650b wheel (27.5") the sirrus has a 700c wheel (29") and a thru axle vs quick release hub. (incidentally both are 135mm rear hubs though)
Fork/ headset - won't fit - the demo 8 has a 1.5" headtube the sirrus a 1 1/8" headtube.
Bottom bracket/ cranks - won't fit - the demo 8 has a press fit bb and 83mm crank, the sirrus a threaded square taper bottom bracket.
Brakes - won't fit - the demo 8 only has posts for disc brakes the sirrus comp has mini v brakes.
Drive train - some will fit - you will be able to reuse the chain, cassette, rear derailleur and shifter (although not a trigger shifter, it could work). Cables will need to be replaced and significantly longer on the demo 8.
Seat post - won't fit - different size.
Sundries - so you would be able to use your seat, pedals, grips, stem and bar (if you bought a single crown fork). Although if you were buying a 200mm travel fork to match the demo 8 you'd require a direct mount stem and thicker bar.
I think the simple answer is decide what you want a bike for, sell the one you have and buy one that suits. If you want a full suspension bike to ride on the road I suggest you look at a low travel 29" full suspension XC mountain bike as a starting point.
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).