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His main interest and area of research is in burr puzzles and packing (box-filling) puzzles. He published articles in the Journal of Recreational Mathematics on the Six-Piece Burr and published two booklets, Holey 6-Piece Burr! and A Computer Analysis of All 6-Piece Burrs.
Cutler has designed a wide variety of burrs in addition to his well-known (within the world of metagrobologists) work on the Six-Piece Burr.
He was mentioned in the season 5 finale of Numb3rs for his burr puzzle research. His work on burrs is also referenced in "The Puzzling World of Polyhedral Dissections" by Stewart T. Coffin.