What if I don't send the complete amount from my paper wallet? I have been trying to understand the concept of paper wallets. They seem to be secure in the sense of holding our bitcoins but no so much when we try to spend the bitcoins from the paper wallets. Now, I am supposed to transfer all the bitcoins from my paper wallet at once while importing the private key in blockchain.info. But what will happen if I spend a little bit from it?

From what I understand at this point, the rest of the amount won't be present in the paper wallet address. It will go to a "change" address. This is where it gets all confusing. How will I get access to the rest of the bitcoin amount then?
When you make a transaction, you will make a change output. This output can be to any address that you want, just as if you are sending Bitcoin to someone else. Depending on the software you are using, you can set the change address to whatever you want. You could send the coins back to your paper wallet address or you can create a new paper wallet and send the change there.

It is recommended that you do not reuse addresses, so you should create a new paper wallet and send the coins to that address.