So if it's damage that you are rolling high on, just use average damage for monster attacks. Or, if, like me, you still want dice, but with less swing, you can use the average for some of dice in a roll and roll the others, or you can use smaller dice. Or a combination of both. For example, instead of 5d8 (max = 40), you can use 3d8 + 9 (max = 33) or 1d8 + 18 (max = 26), or 5d6 + 5 (max = 35), or 5d4 + 10 (max = 30), or 3d6 + 10 (max = 28), etc.
In case it's not obvious, the calculation for using smaller dice is really easy: for each die, for each step you decrease its size (d12 -> d10 -> d8 -> d6 -> d4), just add 1 to the constant. So if you start with 4d12 and want to use d6s, that's 4 dice times 3 steps of size decrease, giving a constant of 12. So you could use 4d6 + 12 instead of 4d12.
Not much you can do about attack rolls, unless you start fudging them, but, personally, I am averse to that.
However.
I do kind of wonder if high dice rolls are really the problem. You'll probably get more useful advice if you can give a bit more information about the circumstances. How experienced are your players? What classes are the PCs? What level(s) are the PCs? Describe the encounter that resulted in the most deaths. (Not a blow-by-blow account, just what monsters they were facing.)