Can I delete photos from my phone after uploading them without deleting them from Dropbox too?

Natalie R., unless I'm misreading your question, the answer is as simple as copying all the files in your Camera Uploads folder to a connected external drive on your computer (Mac or Windows). In other words, all those files in the Camera Uploads folder are already (or should be) automatically synced with the \Documents\My Dropbox\Camera Uploads\ folder on your computer's hard drive. Simply navigate to that folder, select all files (Ctrl-A or Command-A on Mac), copy them (Ctrl-C or Command-C) and navigate to the external hard-drive location where you want to copy the files and paste them in that location (Ctrl-V or Command-V).