Removing guns (or at least access to them) can actually reduce the rate of suicide. Guns are quick and easy to use to commit suicide, whereas many other methods take time to set up and don't work as often. When someone is feeling suicidal, often having that little bit of extra time can let the feeling decrease enough to prevent an attempt.

Of course, removing access to guns doesn't fix why people feel suicidal in the first place. That is a whole nother can of worms. But I expect everyone agrees that reducing the number of suicides is good.

RAND: How Gun Policies Affect Suicide

The consensus among public health experts is that there is strong evidence that reducing firearm suicides in contexts where more-lethal means of attempting suicide are unavailable will result in reductions in the total suicide rate (see, for example, Office of the Surgeon General and National Action Alliance for Suicide Prevention, 2012; World Health Organization, 2014; for review, see Azrael and Miller, 2016).

Save.org: Restricting access to lethal means:

Research has shown time and again that restricting access to lethal means or “means restriction” can saves lives. By restricting access to firearms and other highly lethal methods the decline in suicide rates by that method and overall suicide rates begin to decline. Restricting access to lethal means does not always lead to fewer deaths, but is one suicide prevention measure that merits further research and more individual-level intervention training to make lethal means less readily available.