What is this wood joint called?
The 2x4s are joined with a half-lap joint (or a variation on a scarf joint). It's unclear from your diagram if there is any joinery holding the 2x4s down to the 4x4 or if they just rest on top of the post. 

Not sure what you mean by a "regular saw", but half laps can be cut by most saws - circular saw and table saw are most common, though you could use a handsaw as well. Simply run the saw across the board multiple times, removing a sliver each time. A bandsaw (or jigsaw with a long enough blade) could be used by tipping the workpiece on its side and cutting the material away that way. 

You could also use a chisel to cut that joint, as well as a router.