To export a Smart Form you need to do so through the REST API from Workbench. This method requires saving the JSON data of the Smart Form into a text file. 

Navigate to Workbench

1. Navigate to Workbench on the web and login to the Salesforce Org you are exporting from in another browser window.

This method of export will always export the most recently published version of the Smart Form.

2. Navigate to the Utilities tab and open Rest Explorer. Select GET as the HTTP request.

3. Change the URL to: /services/apexrest/axsy_forms/form/<form ID>

<form ID> is the Salesforce ID of the Smart Form you want to export. The Salesforce ID can be retrieved from the URL when viewing a Smart Form in the Salesforce web UI, i.e. the text between axsy_forms__Form__c/ and /view

4. Select Execute and then Show Raw Response.

5. Copy and paste the Raw Response into a txt.file - only the JSON that comes after the HTTP headers and save the file.

Now you need to import the JSON of the Smart Form into the target Org. Please see this article for more information on this: Importing Smart Forms