It depends if your carrier and firmware support wifi calling, such as Tmobile and I think Sprint. If so, you can set it to only use wifi calling and can turn off mobile data if you want and then it will send everything over wifi. If your carrier doesn't support it or you are running non-carrier firmware, then you have to use mobile data to send MMS.
Btw, I don't know what country you are in or what carrier you have, but if the reason you don't want it to use data is because of a data plan limit, in most cases MMS data is not applied to your data plan. It needs the mobile data connection to be sent and received but carriers do not charge you data for MMS - instead they apply MMS to your sms/mms plan charges.
So if you have unlimited text/MMS you will not have any extra charges. If you have a plan with a limited number of text/MMS then you will not be charged data for it either but your MMS message will just count as 1 message towards your monthly limit. If you are not in the US or not with a major carrier, then you should verify with your carrier if that is true since I've only used US carriers, but that is how it has worked at every carrier I've had.