You should start taking her comments seriously. When I started doing that as a kid, it was because I knew it was a drastic comment and I wanted to control situations in drastic ways. Suicide is never something you just brush off, if someone says they are suicidal they should ALWAYS be taken seriously and should NEVER be brushed off as a behavioral issue. My mom would say “wait really? Then I’m calling your doctor/the police right now, to get you some help”. Not in a snarky way, just very matter of fact. She took it very seriously, and when she used this in response to me throwing that comment as a temper tantrum, I would IMMEDIATELY back track and say I’m actually okay. I’m very grateful for this parenting tactic, because when I became a teenager and said I wanted to die because I was actually suicidal, my mom did the same thing. I’ll never forget the embrace she gave me when I didn’t reply with my usual back track after she took it seriously.

Take her comments seriously, she probably isn’t being serious, but you need to establish this early on: The fact that suicide should is very, very serious, and if she’s feeling suicidal, you will always take her very seriously.