Is Junkrat's Rip-tire destructible and/or is it destroyed upon his death?

The Rip Tire actually has an HP bar which means it can tank a certain amount of damage before it blows up. It has 100 effective HP. This means that you can shoot at it to blow it up, explosives also seem to work better against it to blow it up early. High speed, large splash area and early trigger possibility means, in general, you should try to get far away from the sound so you have more time to blow up the tire.

The information presented in the other answer is factually incorrect. If Junkrat dies while Rip Tire is still in play, it will not be automatically be destroyed, and can still be controlled until either its duration runs out or it is destroyed.

Source:

• When used, you will be able to control the Rip-Tire while your Junkrat character stays still and is vulnerable while you control the tire. If Junkrat dies, you will still be able to control the tire until it explodes.

Upon detonating the Rip Tire or having an enemy destroy it, if you have died, the screen will show your dead body, then show the killcam for it.