TOS was constantly finding excuses for Spock to beat up Kirk, in "The Naked Time," "This Side of Paradise," "Amok Time" . . . whenever he was emotionally compromised in some way.
I always figured Spock smacking Kirk around the bridge of the new Enterprise was basically a homage to those scenes.
And the original Spock was certainly capable of expressing irritation on occasion. For example: just look how exasperated he gets with all that bureaucratic stonewalling in "Mark of Gideon." Not to mention the way McCoy gets on his nerves in "The Tholian Web."