I wrote two blog posts in the past regarding similar goals for PowerBI Report Server which can be seen here:

Disable Download Button on PowerBI Report Server: https://bahtisametcoban.home.blog/2019/07/15/disable-download-button-in-power-bi-report-server/

Disable Print and Export Data Buttons for PowerBI Report Server:

https://bahtisametcoban.home.blog/2020/06/04/disable-print-and-export-data-buttons-for-powerbi-report-server/

This time, we would like to control the option to export data from PowerBI report visuals.

In PowerBI Service, this can be achieved by changing configuration in “Tenant Settings”. For On-Premise PowerBI Report Server, you need to connect to Reporting Service instance using Management Studio.

 Steps:

1. Open SSMS, choose “Reporting Services” for Server Type and connect to Reporting Service as shown in Figure 2. You may also use Web Portal/Service URL to connect to it.
2. Right-click on Servername in Object Explorer and click Properties.
3. Click “Advanced” Tab
4. Under “Other” section, Set “EnablePowerBIReportExportData” to “False” to Disable data export. Set it to “True” to Enable data export.

WARNING: This field is not a Dropdown list, instead a simple text box which can be edited directly!