The Mishna says that one who is on his way to shecht the korban pesach or do a bris milah and remembers having chometz at home, if there is time to return, destroy and still be able to do the mitzvah, that is what he should do. However, if there is a conflict so that by returning to destroy the chometz he will be unable to perform the mitzvah, he should just be mevatel the chometz and continue with doing the mitzvah. The rationale is as Rashi explains, since bitul is sufficient m'doraysa, chazal did not impose the requirement to destroy chometz if it will interfere with a mitzvah. The implication certainly is that in a situation where one cannot be mevatel their chometz because it is after the z'man issur, they will need to go back and destroy their chometz even at the expense of the mitzvah. Nonetheless, this point is a machlokes between the Magen Avrohom and Even Ha'Ozer. The Magen Avrohom says he would go back to destroy the chometz but the Even Ha'ozer says he would continue with the mitzvah and leave the chometz at home.
The Tzlach asks on the Even Ha'ozer, since the mitzvah we are speaking about is korban pesach, how can we allow him to shecht the korban pesach while he still has chometz since that will be a violation of a la'av of shechting the korban pesach while he has chometz? The Tzlach points out that in this situation it is not possible to suggest that the aseh of korban pesach would push off the lo ta'aseh of shechting the korban pesach while he has chometz because the concept of aseh docheh lo ta'aseh applies only when they happen to conflict, but a lo ta'aseh that specifically refers to the issur of having chometz in one's possesion while shechting the korban peach, cannot possibly be pushed off by the mitzvah of shechting the korban pesach.