You can kill any Apple Watch app at any time by force quitting it. Though the implementation differs slightly, the idea is the same as the iPhone or iPad. More importantly, it's every bit as simple and easy to do.
How to force quit Apple Watch apps
Note: You have to be in the app you want to force quit before starting.
- Press and hold down the side button until the shutdown screen appears.
- Release the side button, then press and hold the Digital Crown to force quit the active app.
If force quitting apps didn't alleviate the problem, you can always take your troubleshooting to the next level and reboot your Apple Watch.
Updated January 2018: Added alternative suggestions for shutting down Apple Watch apps.