The attached image shows a Scissor truss that is a bit odd. Notice the peak of the ceiling below does not align with the peak of the roof above. This truss does span from the two exterior walls of the house. Not sure if this then causes the drop down section on the right side to become load bearing or not - it does come down to a load bearing wall that separates the kitchen with cathedral ceiling from the hallway with 8' ceiling, but my thought it is that it is simply for the 8' ceiling. Also notice that the drop down portion on the right which serves to mount the drywall for a typical 8' ceiling has no webbing at all - just verticals coming down off the bottom chord of the scissor truss. Lastly, this drop down portion is all 2x4 while the top and bottom chord of the scissor truss is 2x6. you can see from the diagram also the portion that we are wanting to remove so we can 'raise' our ceiling to match the cathedral ceiling in the kitchen.
The part you want to remove appears (per the drawing) to be non-structural. The lack of diagonal bracing (web members) and the fact that the verticals do not connect coincident to the web connections above are strong indicators that it's just to support the dropped ceiling, and can be removed without issue.
If the trusses supporting your ceiling in the kitchen area you want to match look like the truss here without that part, that's another indication.
Those members are not structural and can be removed.
Truss members are either in tension or compression. When a load is added between connection points, it puts the member in “double bending”. That is to say, the member now has additional tension or compression.
To confirm the structural adequacy of the truss without these other members, I’d take your drawing to a local truss manufacturer and have them duplicate a truss that matches your drawing. They have software that can duplicate your drawing and let you know what the live and dead load is on each member of your truss, whether they designed it originally or not.