How do I remove photos from my phone to creatte memory space but back them up to my cloud storage?

In addition to what Lawrence correctly suggests, you can upload the photos from your phone to your computer directly and store them on your computers hard drive. Or you could use a backup service, such as Dropbox or Carbonite or even Amazon Photo if you're a Prime customer and then delete them from your phone. But they will no longer be in iCloud. They'd just be in an actual archive of your choosing.

Here is how you can upload photos from your phone to your computer --> Transfer photos and videos from your iPhone, iPad, or iPod touch - Apple Support

The general answer is you can’t, as iCloud is a syncing service, not an archiving service. However, you can enable Optimize iPhone Storage (in Settings/Photos), which will upload full size images to iCloud, but keep lower resolution photos on your phone.