SOLUTION:
First, always run a sample on similar leather to be assured the design contains the appropriate style parameters.  You don't wish to destroy an expensive leather garment!

Always use a backing, such as a lightweight tear-away.  Even though the leather doesn't need stabilizer, the backing will help move the hooped fabric smoothly and protect the machine from leather particles that may shred and fall into the bobbin area.

If a needle is not the correct size, it might not make a hole large enough for thread to travel through easily.  This will cause fraying and breakage.  Different weights of leather will call for different needle sizes; generally, a 7/11 sharp point needle will work for very thin leathers, and increase the size for thicker fabrics, switching to a ball point if penetrations shred or rip the leather.  Very thick leathers may require a wedge point.

Thread types are also a consideration.  30 Wt. is more sturdy than 40 Wt. and will offer better coverage.  Polyester or acrylic is also a better choice than cotton.

If you're experiencing "cut-outs", the design you are using contains too much density appropriate for leather.  It requires less density to avoid the needle cutting the leather like a knife. On designs that require a solid fill, lessening its density can cause unwanted gaps between the lines of stitching, so it will require a thicker thread like 30 Wt. or add a layer of tearaway backing placed on top of the leather, prior to sewing, to help fill in the gaps.  Colored tearaway sheets are available through various supply houses and are excellent for this situation, but even white will work just fine for light color thread coverage. Dark thread on dark colored leather will not show the gaps as profoundly as the light colors, so the use of a tearaway topping is not always necessary.