The word "trim" something means to cut it a little bit:

You need to trim your beard.

Use "trim" by itself to describe the thing that you're cutting. But you "trim off" the part that has been cut away. For example,

I trimmed the branches.

means that you cut the branches of a bush or tree a little bit to make them shorter. However, this sentence:

I trimmed the branches off.

means that the branches have been totally cut off, and aren't attached to the bush or tree any more.

"The excess ___" means something that you don't want or need any more. In the example at top, the artist uses some of the clay to make the pottery. But there's also some "excess" clay which is not needed. That excess clay is "trimmed off".