Mendix is a cloud-native application platform and can run on many cloud platforms. Depending on the cloud platform you are using, you have different sets of options. Each option will have advantages and disadvantages.
The fastest way would be to use your cloud platform to make a backup of your data. The Mendix cloud offers this option from the developer portal. Other cloud platforms that you manage through the Mendix developer portal might have this option as well, but it's not a guarantee.
If the Mendix developer portal does not offer this option, you might be able to find something similar in your cloud providers portal.
If all else fails, you can always use Mendix to create an API that can be consumed by an intermediate program which can then load the data into your MySQL database.