Answer: When only one side of a tree has dead branches is usually due to winter damage or to root damage. Winter winds can desiccate tree branches, and root stress (over or under watering or root rot) can affect only one side of a tree.
Dead maple branches can usually be snapped off - when they're dead, they're dead - but you can also try scraping the bark of those affected branches to see if you can find green tissue beneath the bark. If not, the branches are dead and can be removed. Without digging down to inspect the roots, it's difficult to determine whether the roots are healthy and the branches were killed by winter cold rather than root rot. You might just want to wait and see if the tree recovers and sends out new leaves and branches or if other branches begin to die, as well. Once root rot begins, it's really difficult to control.
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