why is it important to spend the entire amount?
Because the change of the transaction might have gone to another address in your wallet.
After importing the paper key into your wallet and the full balance shows up simply send the amount of money you won't need immediately to a **new** paper wallet and then burn the old one.
Example (using Multibit as an example):
MultiBit 1.2345 BTC
Paper: 500 BTC
you need 10 BTC from the paper to spend it with Multibit, so first import the key of the paper into MultiBit:
MultiBit: 501.2345 BTC <- ok, now you have full control over the entire amount in MultiBit
Paper: --> undefined, don't need it anymore, burn it!
now immediately send 490 BTC to a **new** paper wallet
MultiBit: 11.2345 BTC
Paper2: 490 BTC
Done. Now you can spend your 10 BTC and the remainder is safe on Paper again. The old paper key has become integral part of the MultiBit wallet like all other keys in there, you have burnt the old paper because you need every key only once and this one has now become a key in your regular wallet and not a paper key anymore.