Mulligans
General Mulligans
This deck is very powerful because of both its burst potential and its control ability.
Aggro Mulligans
Against aggro there are two options: control and stabilize, or counter rush with a divine spirit combo. Both work, but against paladin you're far better off attempting to stabilize, because of the numerous high health taunts available to you. auchenai circle is a very powerful combo against aggro and you may want to consider shadow visioning a circle of healing if you have a soulpriest, to better be able to clear the board early on.
Midrange Mulligans
Much the same against aggro, but if you won't feel pressured (i.e. a non-rush midrange deck) Lady in White is a good keep.
Control Mulligans
Against control, it is very easy to win. By playing cards that by themselves don't merit removal, the enemy is forced to waste removal on cards like unpowered steambot and tar creeper. Shadow visioning into divine spirit greatly increases your chance of winning, as you are able to much more effectively burst a control deck from 30+ health.
Currently 17-1 with this deck. 8-1 against odd pally.