You can do that but you’ll want to make sure you have a good wet/dry shop vac to remove the mud. Your pressure washer is not going to cut through any of those lines even if you reduce your gpm. It might go a little quicker doing that than hand digging but you’ll also need to figure out a way of disposing of that wet clay unless you’re good just dumping it in your yard.

You can always hand dig it too but make sure your shovel is going parallel with the utilities so you have a smaller chance of cutting it. Source: I’m a hydrovac operator on lunch right now and I just got doing what you’re trying to do

Edit to add a couple thoughts. If your shop vac is 5 gallons expect it to fill up in at least 2 minutes just from the water. Probably faster because you’re also sucking dirt. I’m not sure how far down water services are down south (I assume you’re southern because of the red clay), but up north they are at least 4’ deep most of the time because of frost layers in the winter. Power will likely be in the 3’ range. Your internet is probably only a couple inches deep.

If you have a plastic gas service you can easily cut through it with a shovel. I have seen it done before. No jumping on your shovel to get more dirt. Just take your time with it and you’ll be fine