They certainly look dead. But to be certain you need to show closer photos of the twigs and buds. (Btw it is a weird looking plum. Are you sure of the id?)

You can also always scratch the twig/branch to see if there is green beneath. Like peeling a carrot, but you only need to scratch a little - not whole strips of bark. Use your fingernail.

If it is brown beneath, that is a good indication it is dead wood.

My 2 plum trees are 18 years old now and they resemble the knarliness of your tree. I too have had to trim off a few branches that were brown and dead annually. My dead branches were due to borers infesting the area where the limb joins the main trunk. Amputation was the only path to take. If your dying/dead branch exhibits oozing holes of sap then borers turning it into swiss cheese could be the problem.