Your tree is alive above the graft. So you can make a new tree out of what's growing. It's fine to cut off the dead trunk.

I'd take the plant back and get my refund. I bought raspberries in those gunnysack packages. I know the package was a gimmick to tempt the unknowing, but the plants were a variety I was looking for and the plants looked really good. So I get them home and the roots are in a plastic bags with about 2 Tablespoons of soil, and the roots are completely exposed. Yikes. I potted them and put them into strict quarantine. I figured anyone who would ship plants like that didn't care if they lived or died and wouldn't care if they were diseased. So far, so good. The plants look great and are growing rapidly. However, I know I bought mine within days of their arrival to the store. If those plants had sat very long in that package, the roots would have been too dried out to live. In future, be very careful about fancy packaging. It's only purpose is to attract consumers. Those raspberries I bought in the gunny sack were extremely expensive for two very small dried out sticks with tiny dried out roots. I knew I was paying a lot extra for the package, but those were the only raspberries of that variety available in the area and many mail order places were sold out early this year. I hadn't been able to find them any place else. That fancy expensive package, by the way, just went into the trash, so I paid a lot for something to immediately throw away.

Have you fertilized it recently, looks very similar to an overdose of food, burning edges, or in this recent heatwave, just scorch of leaves. I had a similar problem on Raspberry canes, same leaf issues, I surmised it was due to the extreme heat of July and perhaps a lack of Iron. I gave them a dose of Chelated Iron, and a 1/4 portion of fertilizer and the remaining canes perked right with with in 2 days. Some of the older bottom leaves still show symptoms, but they aren't photosynthesizing much sunlight anyway, so I removed them. As of today, all new growth appears healthy and vigorous.

Shudavies, not all growth is herbaceous. tps put up shoots also from below the surface. Some people even plant tps at an angle so they will form new plants. This is called layering. This year if you haven't already cut them off wait until the leaves unroll. Then check to see if are from herbaceous or tree. On another site someone mentioned that tps are generally not shiny and herbaceous are very shiny. There are exceptions to this as for everything. If you want a tree form remove the growth if it is from the mother plant. If you want a larger shrub like plant let them grow. Each appeals it is a matter of personal likes.