Can grandparents get a DNA test to prove if they are the biological grandparents of their grandchild?

DNA testing of this sort has to be done through the male parent and his male parent.
If the grandfather fits that condition, then you have to get his son and the child's (male or female) DNA done too, and that would require the co-operation of the rest of the people involved.

It can be done but why, is there an issue ? Is one of the parents dead and the grandparents are trying to get visitation ?

Can grandparents get a DNA test to prove if they are the biological grandparents of their grandchild?

Why? It matters.

(I'm a step Grandmother. My grandchildren - and they are my grandchildren - don't care. I don't either.)

I think it's possible to skip the bio father's DNA and get the DNA of the bio father's father and the child (of either gender). But paternity DNA testing can ONLY be done through the male lineage.
Again, if other parties (usually the mother) won't agree to have the child's DNA tested, there is nothing a possible grandparent can do.