no. not usually. What brand , type or model valve. However, I frequently shut off the main when doing most supply oriented work just tio be on the safe side

Thank you for your quick answer. I will turn the supply off to be safe.

Do I need to turn the water supply off to remove a shower diverter valve?
Not if you leave the hot and cold off when the diverter stem assembly is off. (see image) What's your complaint? Back to you, Tom

Jazman, now you are out of your element here with plumbinbg advice. You should take a close look at Tom's image, diverter is after the hot and cold valves and will have no water coming to the diverter. The OP said supply, which in our field, means the house main. Stick to tile.

As Bob and Tom stated, and explained, no, on most faucets, you don't need to turn the water off to the valve. However, as also stated above, its never a bad idea to shut the water off just to be on the extreme safe side. Always better safe than sorry.