If chewy gets killed let say 501 legion on first strike does he still do his action?

unfortunately no - his effect is a reaction so it would trigger after the damage has been dealt. If the damage is enough to kill Chewy, like it would be with the 501st, then Chewy is immediately discarded and cannot execute his reaction.

Thanks

You can roughly consider destruction as a kind of forced reaction to having damage equal to damage capacity, with the extra caveat that it is the first reaction that happens (the game itself gets the first chance to react before the players or something like that). Nothing in the rules words it this way, but it's a useful model to visualize the timing of such situations.