DR-880: Understanding the Internal Memory
The memory in the DR-880 is [mainly] used up by the amount of content that's in your user patterns. You have approximately 30,000 notes/events available. Each time you press on a drum pad during recording, it's taking away a note (or more). This is how it's possible to use up the memory with only a few patterns/songs. It's not the number patterns/songs you have, it's the content within them. Deleting unwanted patterns is the one of the ways to free up the memory. Keep in mind though - the patterns are what make up the songs, so if you delete patterns that are used in the songs, then your songs won't have content within them.
You can also consider creating shorter patterns that have reduced content in them. This minimizes the use of the available memory.
For example, if you need to create a section in a song that is 16 measures long, it would save memory by creating a 4 measure pattern (not 16 measures) and play that pattern 4 times to cover the 16 measure section.