Hello!
I can provide you a script to accomplish this task - the requirements for running would be simple:
Python 2.x (2.4+)
Geographiclib extension library (for Python)
Python is compatible with Mac-based OS's. The script would procedurally slice through the coordinates in the KML file and reference the distance from one to the next. If it does not exceed 10 miles, it will store the coordinates and move on to the next. The successive check would continue until the 10 mile requirement is satisfied by adding together all previous distances, at which point it would write a new KML with the original file name plus an incremental integer with only that 10 mile section. From there it's rinse and repeat.
Ideally you could provide the KML so that it can be tailored specifically to that file, though it is not required. At minimum, it would be helpful to know if the coordinates in the KML have altitude data associated (even if the value is at 0).
As far as execution is concerned on your side of things, I am not familiar with how Macs work; though with a short search I'm certain I could find a way for you to execute it without needing to do a command-line prompt. If need be a small, simple user-interface could be scripted as well to ease the use - it's all your preference.
Please let me know if you have any questions.
Respectfully,
Jake Thompson