Take a step back.
She might or might not be making things up, but how old is she? 16 as well? She's been going out with a boy her age, she's slept with him (possibly her first sexual experience), and he's dumped her after a few months. That's what you know. It doesn't sound particularly respectful to her.
Many women get clingy after they've slept with someone. They're more likely to get emotionally attached, and to act out if they don't feel that emotional attachment is being reciprocated.
You and your DS are not to blame if she's suicidal (you are never responsible for someone else's mental health), but I do think your DS needs a conversation about respect for women. Consent is essential, but it's more about just consent in the moment - if he's to grow up as a decent man, he needs to think about why she's saying yes, and if that's built on any untruths.
Sometimes a woman will say yes to no-strings-attached sex and it's OK to take that consent and enjoy it. Sometimes she will say yes because she thinks her partner has deeper feelings for her than he actually does, and if he's a gentleman and he knows that, he will gently take that consent and decline it.
All of the men I know who have ever cheated are men who saw their mothers being cheated on by their fathers. Without exception. If your DS knows why you and your ex broke up, I would say he's at prime risk of becoming a man who doesn't treat women well, and this is an opportunity to make sure he doesn't continue on that path.
If you do believe his side of the story, I don't think it's overstepping your duty as a woman to tell him you believe him but to help him find some empathy and compassion for how the girl is feeling, and to ask him to think about how he would handle things differently next time, knowing what he does now. I assume you've already discussed safe sex with him, including pregnancy and STIs, but if not, that's also an awkward conversation you need to have.
It's really not rocket science to expect that a 16-year-old girl (or worse, a 15-year-old girl) who has sex with her boyfriend and is dumped shortly thereafter is going to lose it emotionally. She's still a child, she's still going through puberty and learning how to deal with big feelings. And being dumped after a few months feels pretty shitty no matter the age.
He wasn't necessarily wrong to leave her, but I do wonder if he should have slept with her in the first place. Like I said, it's about more than just consent in the moment. Consent in the moment is the legal minimum. It takes more than behaving the law to be a gentleman, and that's how we should raise our sons if we want to make the world a safer place.
So, no, I don't think you should punish him per se, but I think you should have a pretty awkward conversation. I guess for a teenage boy, that sort of talk is punishment in itself. Honestly, OP, I think this is a sliding doors moment for your son. He can either take this experience and learn how to treat women better, or he can dismiss it as 'well, that girl was crazy' and grow into the sort of man you really don't want him to become.