Sometimes they can look dead and not actually be - buds may have frozen, so it will take awhile to grow the second set. Scratch the bark (to check for green underneath) to be sure first, just above where you think the trunk has died back to, but if it is dead, then yeah, cut away. In my amateur opinion any way.
Yes, chop it! There is a dark patch under the bark in the second internode above the living branch and this seems to possibly be the reason for the failure of the tree above this point. You will probably get a lot of sprouts emerging around the base of the good branch (there is one there already) and these will want rubbing out to promote good structure. Leave a sprout or two from lower down if you think a branch in that area would be beneficial. If the roots are good and healthy you will see some long growth from the main branch and it would likely give the best results if you stake this branch in an upright angle to become the new leader.
Maf, Thanks a lot. I chopped it. I'll cross my fingers and hope for the best. I'll post some pics later in the season. Cheers! Pat
Purple Ghost is one heck of a plant, in my opinion. I have two and my first I had to chop off the top. In a few years you would never know it. I almost took it out and threw it away (which was why I bought a second), now I'm glad I didn't. In fact, I have really been impressed with all the ghost series here in Illinois where winters can be challenging for Japanese maples.