Let's consider the variant of dominated strategy which is the pure strategy that is not a best response to any mixed strategy of the opponent (two player game). Intuitively it sounds like more stronger notion of dominated strategy, because in this case all mixed strategies of the opponent is taken into account, lets call this kind of dominated strategy as "useless strategy".
Obviously "useless strategy" doesn't participate in mixed strategy of the player, therefore it can be safely excluded from the game.
Is there any algorithm to detect "useless strategies"?
A strategy that is never a best reply to a mixed stategy of the other player in a two-player game is exactly the same thing as a strictly dominated strategy.
This result goes back to a paper by Pearce on rationalizability. For a simple proof, see Lemma 60.1 in A Course in Game Theory by Osborne and Rubinstein, where it is shown using the minmax-theorem.