It is OK to cut the stud, as long as you frame it up properly afterwards. There is no significant weight sitting on that one stud. Cut a strip of the drywall, 3" larger than your vent pipe, from the stud on the left of the one to be removed to the stud on the right of it. This piece can be reinstalled after you are finished, so be careful (there may be a screw holding it to the center stud). Make a frame of 2X material, depending on what is already there (2X3 or 2X4). You will have two long pieces, fitting from one end of that stud bay to the other, and four short pieces, the length of the vent pipe diameter and fitting on both sides of it and on both ends. Remove the center stud from that space you cut and install the new frame in that opening (Don't forget to replace the insulation). Replace the drywall piece that you removed and tape and spackle the seams. Cut your hole for the vent pipe, and you are all set. Put caulking around the pipe that exits outside.