Unpair Apple watch

If the watch has "completely" failed and has no life at all you probably don't need to do anything to the watch. All you would need to do is remove from your iPhone and Apple ID. Just follow the relevant steps in Apple's support document,

What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support

Also note the link at the bottom of the document, about recycling the retired watch. It might not work for you sny longer but its components can be an important contribution to the next generation.

With a web browser, go to: https://www.iCloud.com and sign in with your Apple ID. Open Find My iPhone and select All Devices (at the top). Then click your Apple Watch, select 'Erase Apple Watch', and select Next until the device is erased. Finally click "X" next to remove your Apple Watch.