Diamoci is reflexive (diamo a noi stessi = give to ourself). Diamoci is used as a sort of exhortation in some expressions: Diamoci una mossa = let's move! c'mon! Diamoci un'occhiata = let's look into it Diamoci una svegliata = let's wake up, let's move, hurry up! Diamoci un taglio = enough! stop! Even if "ci" means "to us", in these expressions wants to soften the phrase and been less direct. A: Arrivo, sono quasi pronto / I'm coming, i'm almost ready B: Ok, ma diamoci una mossa / Ok, but hurry up B wants A to be faster, but he/she doesn't want to be too direct.