Q.Dogwood problem
I transplanted my mother’s dogwood last spring. My mother passed and I wanted to keep her dogwood in remembrance of her. It lost all its buds but it did leaf out shortly after. This year it seems that its branches are dead. Is there a chance it could of survived? Should I prune all the dead branches?

Was the tree still dormant when you moved it, or had it began to leaf or even bloom?
Dogwood can be transplanted, but usually should be done as the plant is dormant. Did you root prune the tree?
Was the tree well watered to help establish root growth?
Do the branches snap or bend? If your finding any bending branches or some green if you scratch the bark; there may be life still in your tree.
Nearly the entire United States suffered a very cold long winter. If the tree had not been able to establish a good root system and the effects of the weather, it's entirely possible your tree may have not survived.
I would not trim anything on the tree at this time. Wait and see is your approach right now.
Here are some links with Dogwood care.
https://www.gardeningknowhow.com/ornamental/trees/dogwood/caring-dogwood-trees.htm
https://www.gardeningknowhow.com/ornamental/trees/dogwood/dogwood-tree-transplanting.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/winter-damaged-trees-shrubs.htm