hard to tell much of anything on these pix.. and im not sure you can do it with pix .... so an onsite inspection might be best ...

whats the deal with the thuja or whatever to the left in the first pic when expanded?? .. against the fence???... why is that one all brown also??.. might be a clue ... how about a pic of that ...

nice lawn ... is it new.. ...whats sprayed on it ...

all that said.. BEs night not be the best tree for a small suburban yard... you might want to consider removal.. which of course.. will solve any other issues ...

i have a huge one out near my pole barn.. and in bad years... is have BE bugs just about covering the barn ... have you experienced that yet???

i cant see a leaf.. i am depending on your ID ..

i also note.. it seems to be growing at quite an angle.... is it growing out of shade from a neighbors tree????

ken

If the branch is entirely dead all the way to the trunk, just prune the branch at the collar as proper procedure would dictate, not leaving a 'stub' but not gouging into the bark either.

It only a portion of the branch is dead, prune back to where the dead part ends and the healthy part starts.

Proper branch removal: (safe site)

Judging from your picture of the trunk, there have been many lower branches removed from this tree over the years.

One possibility is, the lower branches are in the shade and are the ones to die out first.

eta: i'm not a fan of Box Elders myself and would never plant one in my yard for the reasons mentioned above. And it's easier to remove a smaller tree than one that grows to large proportions.

Like all maples, box elders are very susceptible to Verticillium wilt, which will frequently cause midseason branch dieback as illustrated by the photos.

Pruning out affected branches will not have much impact on the control or spread of the pathogen but it will improve appearance.....at least temporarily. Be sure to thoroughly sterilize any pruning equipment after usage on this tree to prevent spreading the pathogen elsewhere.