1. You cannot stop all evil. There are those evils that can be stopped by committing another evil; and, there are those evils that can be stopped and prevented without committing any evils. The focus needs to be on the latter.
2. Subjecting everyone in the population to mental health screenings could reasonably be argued as an evil. Preventing one's actions based on something out of their control, could be argued as an evil.
3. Not everyone with mental health issues will be compelled to kill others. Thus, taking guns out of the hands of all individuals with mental health issues is both unfair to and an offense against those who would never be compelled to kill others. It would be an evil.
4. Restricting someone who is on the verge of killing others might actually be argued as legitimately good for said person (it is an interesting debate as to what restrictions actually benefit an individual's autonomy; I think that restricting one from murdering others is a restriction that does benefit that individual's autonomy).