Moving photos from phone to Mac

I recently got a new iMac and was hoping to use it to organize pictures and videos from my phone that I use as an artist. But when I logged into my Apple ID it automatically synced all of my photos and files over from my phone and iPad. If I move the photos out of photos and into a new folder on my iMac and delete them off my phone will they also disappear form my Mac? I just want to free up space and organize on my Mac. Its frustrating to have no iCloud space to back up my phone but tons of available phone and Mac space.