Good question. Shehechiyanu is the blessing we say upon experiencing the joy of reaching a new season in life. For example, we say shehechiyanu when eating a new fruit, putting on a brand-new suit, and when doing a mitzvah that comes around once a year.
So why don't we say shehechiyanu on the once-a-year mitzvah of destroying our chametz? Because, although we feel the joy of performing a mitzvah, we are also aware of the fact that we are engaged in an act of destruction.
Another explanation is simply that there is no need to say shehechianu at the time of destroying our chametz, because we rely on the shehechiyanu blessing that we say at the Pesach Seder.
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