How to turn off the Samsung Galaxy Watch 4
If for whatever reason you need to entirely turn your Watch 4 off, there's a couple of quick ways to do that. The first way is to swipe down from the main watch screen and you'll find a standby button a bit like the one on a remote control, which will let you turn off the watch.
Alternatively, you can hold both physical buttons on the side of the watch and that will quickly push you into the same screen.
Source : wareable.com