They will slowly grow back from the new little sprouts if you do not accidentally snap these off while removing the dead original tops above.

In this case where you know that the roots are still alive, I would use the scratch test and carefully scratch the bark with a nail to confirm that the trunk or branch is dead. If dead, then cut it there. The only reason for leaving dead wood would be to provide some stability to the tiny plants now growing (you could put a string between it and the old trunk if it is too stormy windy so it does not toss around much).

Most of my japonicas here did almost fine except for White By The Gate, that was blooming on Feb 16 (the date of the freeze). All growth appeared dead above the soil line. I removed the browned out flower buds around a month ago but kept the plant mulched and the soil moist to this day. Yesterday, while pulling weeds nearby, I noticed some leaf out from the base of the trunk at a height or 1-2". All right! ;o)) Now it may be a few (???) seasons before it blooms again. I may be doing the same thing as you soon but weeding takes priority. All of the sasanquas were dormant so they had no issues.

Good luck!

So apparently it wasn't Heaven's Gate that it was waiting by after all.