Note that I said 'accidentally injured' in my original comment; obviously suicide is a different matter entirely. This might actually be a controversial opinion, but I believe people who want to end their lives have a right to do so.

Barring that, we already have measures in place (e.g. involuntary hospitalization) for the acutely suicidal. For others, why stop at taking away their guns? Take away their kitchen knives, Tylenol, and spare rope while you're at it. Hell, throw them in a padded cell so they aren't tempted to visit any bridges or tall buildings. Taking away guns doesn't treat the actual problem.