1. Cut out a paper triangle with scissors.

2. Cut off a paper triangle with scissors.

3. Cut away a paper triangle with scissors.

4. Make a cut of a paper triangle with scissors.

(Would you let me know the difference among the four expressions? Are they all interchangeable without changing the meaning?)

Only #1 is correct.

While the four expressions you provided can all be understood to refer to cutting a paper triangle with scissors, there are slight differences in meaning and emphasis:

1. "Cut out a paper triangle with scissors": This expression implies removing the paper triangle from a larger sheet or piece of paper. The focus is on creating the shape of a triangle by cutting along its edges.

2. "Cut off a paper triangle with scissors": This expression also conveys the idea of removing a paper triangle from a larger sheet, but the emphasis is on disconnecting or detaching the triangle from the rest of the paper.

3. "Cut away a paper triangle with scissors": This expression suggests cutting out or removing a paper triangle, but it also implies removing or discarding the triangle from the surrounding material. The focus is on eliminating the triangle as opposed to simply shaping or detaching it.

4. "Make a cut of a paper triangle with scissors": This expression focuses on the act of cutting specifically, without emphasizing the removal or detachment of the triangle. It suggests creating an incision or division within a paper triangle, rather than creating the entire shape.

While these expressions can be understood interchangeably in many contexts, the subtle differences in meaning and emphasis can be important depending on the specific situation or context in which they are used.