Horatio must be holding that cup pretty tightly for Hamlet to have to say this.
It also occurs to me that Hamlet may not succeed in getting the cup. He’s weak, after all, losing his facility with his body, I expect. It’s clearly not having an impact on his mind or his speech. This would mean that the next lines are further attempts to get Horatio to put down that cup. That powers those lines rather powerfully.
I think I’ve usually seen this line with Hamlet getting a burst of energy and getting his hands on the cup. The next lines then become a little speech rather than a plea for Horatio to give up the deadly cup. I mean – I understand why this happens. If Horatio doesn’t surrender the cup, he could look like a real asshole who is teasing a dying man. It’s a hard look to avoid under the circumstances, though.
The Hamlet Project 