External GPU for mining
You would likely spend as much buying a couple of decent GPUs as you would buying a small mining rig for sha256/scrypt (i.e. Bitcoin/Litecoin).

You can use "riser cables" to connect a PCI-E GPU to your computer's motherboard without it being inside the case but there is a limit on how long these can be (safety / fire risk).. I think 12-15" is about as long as they get realistically.

FYI:  GPU mining doesn't need a powerful computer, any old computer will do so long as it has suitable PCI-E ports and a few Gb of RAM.