Thanks for writing! You can definitely prune out any dead shoots every year.
As far as the shoots that aren't dead -- you can cut them back considerably --- to 6 or 8 inches tall for example. If you do that, however, it probably won't bloom for two or three years.
You can also go about it more gradually and cut back 1/3 of the stems every year. That way you'll still be able to enjoy its blooms and in three years it'll be more tidy and compact.
By the way: The best time to prune back most blue- and pink-flowering hydrangeas is in July, right after they finish blooming. You can prune most of the white types in winter or early spring.
Good luck! I hope this helps!
---Justin, Senior Garden Editor, BHG.com