Unless the animal is dying for other reasons. This would lead to a spectacular decay. Is there any whitish material on that arm? I am not sure the animal will have enough food to recover from this, but from the description, it might be worth a shot. There is always a chance, depending on a lot of variables, etc.
If you do it, take a clean new razor blade and make one clean cut, being sure to get to the healthy tissue. Do this as quickly as possible. This would be a hope for the best situation. However, unless you have a refugium or sump to keep him in (with LR), then there is no reason the shrimp wouldn't continue to pick at the (now open) wound.
IMO, you have too small a tank and too little LR to keep both of these stars long term. In order to keep the red star and the spiny for long, you need a large tank with lots and lots of LR, IMO nothing under a 55g...but best success with tanks over 100g. Those guys have the same diet and will probably both suffer from the competition. Have you noticed them eating any prepared foods, or do they stay on the glass and rocks? They are both algal/bacterial film and other encrusting animal feeders, though sometimes poeple report them trying to eat other thing. Anyway, this stuff takes time to regrow on areas the star has covered, and it does take time. With two, it causes some stress- you need a lot of algal/bacterial film to eat! The red Fromia is well known for dying of starvation at the 1 year mark. These animals do not live in close quarters in the wild. Forcing them to in a tank usually does not mean they live long (eg a normal lifespan). Whatever you do, do not add another reef safe star (except brittle/serpents).
IMO, success with reef safe stars is measured by keeping them over 1 year. How long have you had the other red stars?