1. I presume you mean a hacksaw, which would be the right tool.
2. The pipe will have very thin walls. Given that you need to have at least 2 and preferably 3 teeth of the saw in contact with the pipe while cutting I would use a blade with no fewer than 32 teeth per inch. A new fine blade in a mini-hacksaw would be fine. You will need a half round file, or some sandpaper to deburr the cut edges inside and out.
3. Don't underestimate how difficult it is to hold round pipe while you cut it. Wrap it in tape and clamp it securely (without crushing it) if you can, otherwise you run the risk of damaging the chrome. Something like a B&D Workmate with the jaws partially open and parallel is ideal.
4. Personally I'd cut the vertical piece first. Basin flat on the ground. Insert vertical part to lower fitting and, keeping it upright, Swing it sideways to touch the side of the upper fitting. Mark across the centre line of the upper fitting onto the pipe (wrap it in masking tape first). Measure down from the centreline of the horizontal piece to the mark already made. Call this dimension X. Measure "X" up from the bottom of the vertical leg, and mark the pipe (again, taped). Get a piece of A4 paper, fold it in half lengthways and wrap it around the pipe with the folded edge to the mark. Make sure it is straight around the pipe, then mark the cut line. Cut as above.
5. With the cut vertical leg fully into the lower fitting, and keeping the pipe vertical, mark the horizontal leg where it touches the outside of the upper fitting. Measure the depth of the upper fitting, to the stop inside it. Make a further mark near the open end of the upper leg. Use the paper again to mark a circle around the upper leg at the second mark and cut the pipe.
6. When cutting, make a first cut, not all the way through at a point on the marked circle, then rotate the pipe and repeat. Keep doing this, going part way through once or twice more, then again going all the way through. This will minimise the burr on the outside, and makes it more likely you will end up with a square edge.