Head out to the The Highlands Hyperion Bridge Fast Travel Station. You will be contacted by Roland who will tell that the Slab King lost it after Hyperion killed his dog. This Fast Travel Station is only a short distance from the entrance to Thousand Cuts. Just head on up the slope to the entrance of Thousand Cuts. Head on through it to get in and start dealing with everything.
On the other side you will find yourself set upon by the Slabs. They will immediately begin attacking you once you are in range. Turn to the right and start fighting your way through their masses. This will take you through Slab Town. Just keep going to the North. There is no shortage of people to kill. Just keep fighting your way through the markers. This will lead you to Broken Face Bridge. head across the bridge and look for the entrance into the Buzzard Factory. You can't go straight in. Instead you need to take the nearby ramp up and into the building: