You can export the Table Grid data for a single issue or for an entire set of issues. How to export the data for multiple issues?
For example, export a set of issues to see all table grid entries where project = MYPROJECT.
You will need access to the database where the grid table is stored.
Assume that your grid table is called actions_c10123 and is stored in the same database as JIRA then you can export the table rows using a query like below: