You can export Test Cases from the following screens in Jira:
Export from Jira Issue Screen
Open a Jira Issue
Go to Vansah within the Issue
Now find and select the Test Cases you wish to Export
Click on “More Options” in the top right hand section then select Export

Now you should be able to select either option:
1) Test Cases (All Fields for a Test Case apart from the Test Script)
2) Test Cases and Test Steps or
3) Test Cases, Test Steps and Results

4) Select Next
5) Now you can choose the File Type you wish to export the cases to. You may export Test Cases into the following formats: XLSX, CSV, TXT, or a XML

Export from Vansah Board
Navigate to the Vansah Dashboard under your Jira Project
Find your Test Cases and select the cases which you wish to export. Follow the same process to export your selected Test Cases.