MacBook Pro 2014 not booting after El Capitan 10.11 update
Yes - you have many options to back up a Mac that won't start.


you can start the Mac in Target Disk mode and connect it to another Mac to do the backup. 
you can bring a USB drive and use internet recovery to install a working OS on to the new drive. Boot to that and then perform the backup.
you can get help at https//locate.apple.com
you can even try reinstalling the OS on top of your current OS. That might fail and might make things worse if the problem is a hardware issue (failing hardware) so I've listed this last.


Which you choose depends on your expertise, amount of time you care to invest, speed of your network and whether you can isolate why the Mac isn't starting. Knowing that might allow a more surgical repair instead of starting over. I'd say get a backup and then decide how to fix things as a follow on step.