There is no need to manually destroy the Animate script, you can remove the Animate script from the character by placing a local/server script named Animate in StarterCharacterScripts, and you can also implement animations yourself there.
The Animate script you created can also be disabled, and it will be guaranteed not to play any animations too.
The easiest way to make your own alternative animations is through forking the Animate script from the character into StarterCharacterScripts, and editing the StringValues under it:
I remove my player’s “Animate” script through their character in workspace. A solution that you could use is to check for a character (perhaps through Player/CharacterAdded) and remove the said character’s default animation script.
A bit of a hack or oversight, but it doesn’t need to be a script. I insert a BoolValue named Animate to get rid of the script the same way, if needbe. It checks by name to determine if the script should be inserted or not.