How explicitly can the blockchain be pruned? How can the blockchain be pruned?

If the blockchain is tamper-proof thus cannot be changed, how can the data be removed?

Please be as explicit as possible.
The blockchain itself cannot be pruned.

Each block is verified through hashing all its data and a random nonce to find a hash that has a certain number of leading zeroes. If you even removed a single little bit of data from a block, the resulting hash would be changed. As most likely the new hash would not fulfill the difficulty requirement, the proof of work would have been destroyed. You'd have to create a new block to take its place. Then however, you would also have to recreate all subsequent block, as the parent's hash (think of it as a fingerprint) is included in its children block, i.e. if you change the parent, the whole blockchain succeeding from it becomes invalid as well.

What can happen is that the database of verified transactions that Bitcoin-Qt clients store is pruned. So far, after verifying each block, full clients keep every transaction that has ever happened locally. Instead, you could only keep the transactions in your database of which the outputs have not been spent yet.