Is it unsafe to remove one stud from a load bearing wall?
The opening you want to create has to be framed like a window as shown*.



Notice the addition of a header to carry the load of the cut stud (cripple stud) to the sides, and the added jack studs which support the header. Because you're only supporting a light weight cabinet rather than a window, you probably don't need the double sill (single will do).

As pointed out in the comments, you can't simply cut a load bearing stud without any issues. Some sort of temporary support must be put in place to carry the load before you cut into existing structure and not removed until the new structure is in place.