Do they cancel each other out?

No they do not. Here is a topic I had to make when I got that result with one of my players:

Hope it helps.

They do not cancel their Triumph and Despair specialty results. They would cancel one another when used as Successes and Failures.

The Success part of a Triumph can be canceled by a Failure. The Failure part of a Despair can be canceled by a Success. However, the Triumph and Despair parts cannot be canceled.

After a year and a half of this game we finally had that result twice this week. Nothing too exciting came out of those rolls for our group, one was a crit and ran out of ammo at the same time, but it was somewhat commical to see our party go all three stooges with the Despairs.