Can I physically split a SQL Server database?
Yes, is possible to move old data to filegroups that are still part of the database, but store on files located on cheaper, slower, storage, adnd mark these file groups as read-only. You still need to do a full database backup once, but subsequent backups can leave the read-only file groups out of the backup, significantly reducing the size (and time!). I recommend you read Performing Piecemeal Restores.

Another useful feature is partitioning, which allow you to split a table automatically into partitions and place partitions onto this slow, untouched and read-only file groups. See How to Implement an Automatic Sliding Window in a Partitioned Table.