A Stoic answers

How would a Stoic cope with grief?

Stoicism is often misread as forbidding grief. It does not. The Stoics grieved, and said so. What they refused was being destroyed by it. They prepared for loss in advance, by remembering that everything they loved was lent, not given; they let the natural pain come; and they did not add to it the second suffering of rage at reality for being what it is. You loved a mortal thing. That it could be lost was the price of having it at all.
The principleEverything we have is on loan from fortune and can be recalled without notice. The Stoic loves fully anyway, and gives it back, when the time comes, without cursing the lender.

What the philosophers say

Seneca

Seneca wrote letters of consolation to the grieving. He did not tell them not to weep. He told them to weep, and then to stop; that endless grief honours no one, and that we should be grateful we had the person at all, rather than bitter that we lost them.

Epictetus

Epictetus offered a hard but freeing image: never say of anything that you have lost it, only that you have given it back. The one you loved was never your possession, only on loan, and now it has been returned.

Marcus Aurelius

Marcus, who buried most of his own children, met loss as part of nature's order: things change, pass and are renewed. To rage against that is to ask the universe to be other than it is.

Try this

Questions

Do Stoics believe you should not grieve?
No. The Stoics grieved openly. They prepared for loss in advance and refused to be destroyed by grief, but they did not pretend it should not hurt.
What is the Stoic view of losing someone?
That everything we love is lent by fortune and can be recalled. Loss is the price of having loved a mortal thing, and the Stoic gives it back rather than cursing reality.

Ask them yourself

Put your own situation to Marcus, Seneca or Epictetus and hear them answer in their own words.

Talk to a Stoic