I think you will need to provide more details. JMP does indeed correctly calculate a standard deviation. So, a few questions:
* What version of JMP are you using?
* Can you share some of your data, even if it is anonymized? You may have your data formatted in an unusual way.
* How much data do you have for each of these categories?
* Have you verified these exact same calculations with this exact same data in R or Excel?
Remember that there is no requirement that a standard deviation be less than a mean. For skewed distributions, the standard deviation could certainly be larger than the mean.
Dan Obermiller