Since you cannot speak underwater, You obviously cannot cast. But at the same time, if yuo had the Silent spell feat((the feat that allows you to cast without a verbal component)) Would you be able to cast? I am saying is this, You cannot speak since you are silenced, but a wizard trained to cast without speaking can cast spells underwater.

Being underwater also hinders the arm and/or hand movements (somatic components) needed to cast most spells. Since you can't make your spells both Stilled and Silent at the same time, there are still factors resulting in a good chance of spell failure when underwater.

Thanks