Ah, right now, there really is no ready-built way to have multiple skeletons on one GameObject for 4-direction or 8-direction setups.
This is a conversation people have here in the forums every now and then and there are different approaches that are ideal depending on the character visual style.
For example, if it's simple and forgiving enough visually, and have few-enough bones, you can pose your character's attachments per animation so they will face the correct direction.
If it's more complex and bones can't be reused for every direction you need, you'll need one skeleton for each direction and do those animations. This second solution requires an extra layer of code on top of the regular SkeletonAnimation script, where you can manage which way the character is looking and what animation it should be playing. Then that managing script can hide and show the correct Spine GameObjects and make the correct SetAnimation calls to the object representing the correct direction.
I think it'll be much more complicated with Mecanim but I don't use that much so I could be wrong.