Should I very carefully take the trellis out of the pot that the plant is on and train it onto a larger trellis or just leave it on the small one in the pot and let the plant continue onto a larger trellis?
You can take the trellis out of the pot if you want. Just do it carefully. You didn't say whether or not you live in a tropical area. If you do, you can train your mandevilla onto any trellis you want. If you live in the temperate zone, any trellis you use will have to be portable because you will have to bring the plant indoors in the winter and early spring.