Oakleaf Hydrangia Dead Branches
Was there a problem with soil drainage in the area of your hydrangea? If the soil was saturated for an extended period of time (e.g. during last year's heavy rains) this could have contributed to root decline, resulting in dieback. All you can do is prune out the dead areas during dry weather. If you scratch away the outer bark with your fingernail and see green tissue underneath, the branches are still alive and can generate new growth. If the stems are brown underneath the bark and snap easily, they are dead. Prune them out.
It looks like you have quite a bit of periwinkle underneath the hydrangea. This will compete with the hydrangea for soil nutrients and water, so you should remove it from under the shrub and just put a light layer of mulch, no more than about 2-3" inches deep.