[wladimir]

They're separable in theory, but if you take out 'mining' you'll need to find a different way to create the incentive to maintain the network which also needs a solid proof of work to prevent people from cheating.

Also you'll need a different way to do the initial currency distribution which is also cheater-proof.

These are very hard problems.

[TruthElixirX]

Its already built in. Once all the coins are mined (or it is no longer profitable to do so) one can still run bitcoin but charge transaction fees for processing transactions.