Enable pruning? You can set Bitcoin Core to only use X amount of GB/MB.
-prune= Reduce storage requirements by enabling pruning (deleting) of old blocks. This allows the pruneblockchain RPC to be called to delete specific blocks, and enables automatic pruning of old blocks if a target size in MiB is provided. This mode is incompatible with -txindex and -rescan. Warning: Reverting this setting requires re-downloading the entire blockchain. (default: 0 = disable pruning blocks, 1 = allow manual pruning via RPC, 550 = automatically prune block files to stay under the specified target size in MiB)
To enable pruning use the above command in your bitcoin.conf (If you don't have a bitcoin.conf yet, simply create one.)
Anything above 550 will work.
So if you put 1000 It'll use a maximum of 1GB. (If every block were to be 1 MB that is)
I've bought Antonopoulos' Mastering Bitcoin and there he states that you can install Bitcoin Core and configure it to reduce the size of the blockchain by discarding old blocks, but that it will still download the entire dataset before discarding data (page 38).
I don't think this is true. I'm pretty sure it'll discard data as you go.