The strap and band cutter is specially configured to produce smoothly rounded corners on the ends of a cut band or strap when opening palletized loads and other materials secured together by straps or bands for shipping. The cutter is a manually operated shear having two elongate lever arms joined by a pivot. The arms terminate in handles at one end and cutting jaws at the other. The cutter operates in double shear, i.e., a central jaw having two cutting edges passes through the opposite jaw and its two shear faces. The jaws are specially configured to produce rounded corners on the two cut ends of the strap or band after cutting, thus greatly reducing or eliminating the chance of injury from contact with one of the ends of the cut strap.