Use an edge-beveling tool to smooth the cut edges.
Place the beveler so that the two prongs that form its "V" shape are facing upward on both sides of the leather's edge.
Push the beveling tool away from you along the cut edge of leather, keeping the tool at a 45-degree angle to the work surface. Make sure the leather is held firmly in place by the nonworking hand.
Try a variety of cutting angles in order to achieve the edge you desire.
Expect to see a thin curl of leather come off the surface as you move the beveling tool along the cut edge. These curls can be discarded as you work.