Great work on the presentation, the intro and the tutorial UI in particular are great. I really like the idea of having to use every side of the die before the faces are refreshed, it's a great way to force the player into improvising with different attacks instead of just rerolling to get the best one.
I think if you took away the ability to roll blanks and let the player 'stack' the dice by purposely leaving a specific colour to last it would allow for some interesting strategies - maybe you could give a small damage boost to the last colour you use and then it would become a risk/reward proposition of trying to save a particular colour for last to use against a strong enemy or something.
I also would've appreciated some feedback for when I've completely used up a die, so I could keep track of what abilities I've already used and which ones are left. The delay between input and firing also made aiming a bit difficult.