The Butcher Mod Pack # 2 introduces mods for the OVE9000 Saw. Installing the Fast Motor and Sharp Blade mods will increase the damage of the saw, nearly doubling its damage. With those mods, even without the Berserker skill, you will be able to open deposit boxes in one click.
Another trick is if you have the Bulletstorm skill aced. Description of the skill:
Basic: Ammo bags placed by you grant players the ability to shoot without depleting their ammunition for up to 5 seconds after interacting with it. The more ammo players replenish, the longer the duration of the effect.
Ace: Increases the base duration of the effect by up to 15 seconds.
To maximize the skill's effect duration, you'll need to empty the ammo of your non-saw weapon (to prolong the skill's duration), and leave the saw with just one magazine left and reloaded (so you'd have a full magazine and have no need to reload after the skill's effect ends*).
Then, deploy the ammo bag and interact with it to activate Bulletstorm's effect. While the skill's effect is active (while your ammo won't be depleted), you just need to hold the fire button (no need to click) to open as many deposit boxes as possible.
* Only two seconds of ammo non-depletion time will be added if you completely empty the saw. In exchange, you will have to reload the saw after the effect ends.
Source: Reddit /r/paydaytheheist post by dive_bomber