A Stoic answers
How would a Stoic get over a breakup?
A Stoic in heartbreak starts from the hardest truth: another person's feelings were never yours to control, and trying to hold what wants to leave only deepens the wound. You loved someone, which was good; it ended, which was not in your power. The Stoic lets the pain come, refuses to add the second suffering of bitterness and obsessive replaying, and returns attention to the one life that is still theirs to live. Time and right action do the rest.
The principleYou can control your conduct and your judgements, never another person's heart. Peace begins when you stop demanding that what is outside your control be otherwise.
What the philosophers say

Epictetus would remind you that people, like everything else on loan, can be taken back. You never owned them. Grieve the return if you must, but do not call it robbery, and do not chase what has been reclaimed.

Seneca would tell you the imagination is making this worse than it is: replaying scenes, inventing futures. Deal with what is actually true today, not with the stories the wound is telling you.

Marcus would turn you back to your own conduct: you cannot make them stay or feel, but you can decide who you are in the loss. Be the person you would respect, and let that be enough.
Try this
- Accept the part that was never yours: their feelings and their choice.
- Let yourself grieve, but refuse the second suffering of obsessive replaying and bitterness.
- Cut off the imagined scenes; deal only with what is true today.
- Pour attention back into your own life and conduct, the one thing still in your hands.
Questions
What would a Stoic say about heartbreak?
That another person's heart was never in your control, that loss is the price of having loved, and that peace returns when you grieve without bitterness and turn back to your own life.
Is it Stoic to feel nothing after a breakup?
No. Stoicism allows grief; it asks only that you not be destroyed by it or add the extra suffering of resentment and endless replaying.
Ask them yourself
Put your own situation to Marcus, Seneca or Epictetus and hear them answer in their own words.
Talk to a Stoic