As APEXistud stated, it is hydraulic. The most common failure point in the Miata clutch actuation system is the slave cylinder. It costs about $50 to replace or $20 to repair. It's quite easy to remove and rebuild/replace. If you decide to rebuild it, be sure to inspect the bore for scoring or other damage (corrosion pits especially).
I've had both the clutch master and slave fail during normal use, so both are susceptible. Look below your clutch master. If there is fresh/wet brake fluid below it, chances are it's the master. However, I'm willing to bet the slave is the culprit.