This is definitely possible, it can be done by consuming a rest service which provides SMS services.
The first step is to select an SMS service API that you can integrate into your mendix application. Twilio is a good option as there is a twilio connector on the mendix marketplace which is a great starting point (there are also many other SMS API options out there.)
Once you have a basic SMS sending REST call set up in your mendix app you will be able to see how you could take some user input stored in a mendix object(string, int, etc.) and insert that input into the outgoing REST call.
This is just a general overview but hopefully gets you pointed in the right direction.