Dampé wants to create an automaton that can chop anything in two, so he needs to see a sword-wielding monster, and a special katana.
Where to Start the Quest
Complete the quest Explosions Galore!, then read the "Chop 'em in Two!" entry in Dampé's journal to start the quest.
How to Complete the Quest
Clear 6 different courses in the Slumber Dojo in Kakariko Village. For help clearing the courses, read the Slumber Dojo Training Guides. You will get the Heirloom Katana after you clear 6 different courses.
You can learn the Sword Moblin echoin the field full of boulders that is east of Hyrule Castle, or the Sword Moblin Lv. 2 echonortheast of Hyrule Castle Town. Create an echo of one of these monsters on the pedestal in Dampé's house.
Then talk to Dampé and ask about creating an automaton, then ask for the "chop 'em in two" automaton, and agree to give him the Heirloom Katana.
Quest Reward
You get the Roboblin automaton from Dampé.