The direct answer to your question, is yes, you can destroy bitcoin but not in the traditional sense.
The blockchain holds a record of the coins that get sent in and out of an address. The only way to send coins out of an address is to use the private key that created that address. No private key, no ability to send or verify those coins.
One could potentially destroy coins by sending them to an address that has no private key, or to simply send it to yourself and erase all copies of your own private key. This will result in those coins being lost in that address forever effectively destroying them.
Though technically speaking, theres no real way to confirm that youve deleted all copies of a private key