Create another table where you store the id of the row you’ve displayed.
Then, to select a random row, make a query that left joins the table with your data with the table with the displayed row id’s, where the displayed row id IS NULL (that will give you all rows that haven’t been displayed yet.
To exclude only the last 10 displayed take a look at ORDER BY and LIMIT.
After having selected a row to display, add the selected row id in the new table.