You can manage (i.e. create, update, delete) Test Sets directly through the JIRA's native REST API.
Xray REST API provides the following endpoints.
Test Set Tests
To view the Test associated with a Test Set you need to specify the key of the Test Set you wish you view. To associate or remove a Test from a Test Set you need to send a json with a list of the keys, when associating this keys can be Test keys or Test Set keys but when removing they can only be Test keys. To remove a Test from a Test Set you need to specify the key of the Test you wish to remove. It is also possible to remove all Test from the Test Set.