You can remove them, BUT......you will need to put collar ties in. As your garage is now, the joist going side to side are keeping your walls pulled together. Now if you understand that, step two.....
The vertical 2x's aren't doing anything but holding up the ceiling joist. You could take them out anytime, but depending on the ceiling joist length, the ceiling joist would bow. Next step.....
If you pull out the ceiling joist, look up at your rafters where they are tied into the ridge beam. You have nothing holding the walls, so the rafters at the peak will want to spread. When they spread they will push out on your walls. The more they push on the walls, the more the walls will want to spread your rafters.
Collar ties will remedy that. Come down a foot or so from the ridge and run a 2x4 horizontally from side to side at each rafter, keeping the two side to side rafters from wanting to spread. That's the problem you see with a lot of old garages when they start racking side to side and the walls are bowing out and the roof looks like a swayback old horse.
Almost forgot.......Cut one collar tie to the size you need. Fasten it either at the front or back rafters. Now go to the opposite end of the garage and measure carefully. Make a mark that matches the dimensions of the opposite end collar tie. Now run a chalk line and snap it. Now measure down from the chalk line to your wall. If you want to put a ceiling in, you want the sloped portion on both sides equal, and you want to keep the horizontal top ceiling piece running straight front to back. Nothing looks worse than a racked ceiling.