Hello Claire,
JMP does not read .mat files directly, that is, without Matlab available. You can probably use the built in Python support in JMP 18 to read the files into a JMP datatable. Packages like mat4py or scipy should work. They will read the matlab variables into dictionaries or arrays, and then you can assign those to JMP columns within the Python code. I have not done this myself.
Brian Corcoran
JMP Development