There's no need to wait on cutting out the dead branches, assuming they are really dead (and that appears to be the case). I can't tell for sure what's going on in the picture, but it looks like there isn't much shrub left. Maybe you could take another picture, from a little further out, when you get all the dead branches removed.

I would try to make most of the cuts within an inch of the ground and clear out all the debris when you are finished. Of course, be sure you aren't accidentally cutting off a live branch (can be easy to do).

Cut off all the dead growth now. It's a variegated shrubby dogwood grown for its leaves as well as its red winter twigs. After it has recovered, you will want to cut about 1/3 of its stems at ground level each spring so that it grows new bright red twigs. It can get pretty large, so you might want to dig the whole thing up in early fall and move it at least 3-4 feet from the building.

Here's mine to give you a feel for the size.

Thanks for all the info! I took your advice and chopped down most of the dead. There's some stump left though, also I noticed there were a lot of ants around the base of the shrub. I'm not sure if that's what killed it or if they moved in on the dead wood. And yes there isn't much left =( but I'm hoping I can save it!

ants do NOT kill plants ... unless the dig a giant nest under them... which heats and cooks the roots ...

the ants have nothing to do with this

you did well.. ignore it.. until its time to prune as babs indicated...

google: rejuvenation pruning of flowering shrubs... to learn the concept ...

your biggest problem now.. is that its about 3 feet too close to the shrub next to it... come fall.. you could move one or the other.. for better spacing .... come on back in mid-sept.. with a new post.. and we can help you with that.. if you wish ....

ken

ps: you are going to come to hate that stone... its a nightmare to work in.. lol.. and probably one of the reasons the prior owner left.. lol...

Yeah I hate the stone! its all around the house we're planning on replacing it, and we bought the house as a foreclosure. They started to remove the rock and replace it with that red lava rock stuff now it just looks silly! I'm thinking I'll move the dogwood then, I have a good place for it in the backyard because what you can't see in the picture is there's a 3rd shrub to the left of the dogwood too. I guess they really really liked shrubs lol