When you get in to Recovery mode, you can select "Startup Options" and choose to start in "Target Disk Mode". You can then use a thunderbolt or USB-C cable to connect it to another Mac. (At startup for an Intel Mac, you can press and hold "T" on the keyboard, as this will achieve the same thing. You should then be able to access the drive and delete some files to make space to reinstall the operating system. The will require another Mac computer.
Depending on other start up options, you could also boot into Single User mode, which you can do in different ways depending on the chipset you have: Mac startup key combinations - Apple Support
In Single User mode, you can manually delete files, although this may require a little extra knowledge to get around the operating system.
Good luck!