The answer to your question depends on your setup, how you've configured Photoshop, and the actual external drive.
Typically one would have Photoshop configured to use the internal drive for its scratch disk location, so in that sense you won't overly slow your work down.
However, it's highly likely that you'll notice read/write speeds to be slower when saving and opening files from the external drive, although how much will depend on the actual drive and what you have installed as an internal drive.
For example, if your internal drive is an SSD the difference will be quite noticeable, especially with larger files. However, if your internal drive is only a 5400rpm drive you probably won't notice any difference. And of course it'll be somewhere in between for 7200rpm drives or fusion/hybrid drives.
Regardless of what you do, make sure you have a backup regime in place. So if you use the external for your Photoshop work, then invest in another drive for Time Machine (or other) backups!
- the more RAM you have, the better. Make sure your Photoshop preferences allow as much memory as possible.
- make sure you have a reasonable amount of free space on your internal drive, not only for scratch disk purposes, but also for virtual memory usage.
- you can work with a few files off your external USB as a test before moving everything across
- once again, make sure you have a backup regime in place!