How can I repair decking and a joist damaged by a small fire?
Left the barbecue on too long?

Of course the middle deck boards need to go, but you have the option of splicing the joist.

What you need is a 6 foot piece of the same material, screws and some good construction glue - the kind that comes in a caulking tube, not a squeeze bottle. PL-400 is good stuff.

Cut the new board into 2 x 3 foot lengths, apply glue generously, and sandwich the damaged section between them. Screw in from each side. No need for many or massive screws - that's what the glue is for.

Optional: chisel out the burnt section - makes the smell of freshly burnt deck go away faster. Paint the newly-exposed wood so it doesn't absorb water.

It may be possible to do all of this from underneath the deck, so you won't need to remove more than the damaged boards.