I have a magazine somewhere (Probably Fine Woodworking) that walks you through how to make the necessary cuts for that joint, or maybe just a very similar one. I think almost all of them were made with a backsaw, and a little cleanup with a chisel.
There's actually a lot more long grain to long grain contact than it looks like from that photo, but it's definitely not the strongest joint there is; it's just a way to make a three-way mitered joint and still have SOME long grain contact.