Searched more in the Gear S User Guide, didn't see an option to block/reject callers. Ended up chatting with Verizon Support who were helpful and confirmed that there is no way to block/reject calls on the Gear S - if the call/SMS/MMS comes in directly to the Gear S number.
So, Verizon Support blocked one of the numbers on their end, so that any further attempts to get to my Gear S with spam or accidental calls/SMS/MMS won't go through.
It's not an ideal situation, but in my case I hope its just a few random accidental calls/SMS/MMS where the sender is one digit off on the number and is unintentionally sending stuff to me.
I will also note that the times when I have received the accidental calls/SMS/MMS my Note 4 has either been off, in Airplane Mode, or out of Bluetooth/WiFi range. Since I have Call Forwarding turned on, I think that the Gear S is working as designed in this case. I want to have Call Forwarding on so that if I'm in a location or situation where the connectivity between the Gear S and Note 4 is not available, then family/friends can still reach me.
But, the lack of a Gear S option to block spam calls/SMS/MMS is still something I think that would be good to see in a future firmware update.