If you are using TurboTax Online and haven't gotten to the review section of your return to pay for the software, you can simply leave that one for now and click on "Start a new return." Once that new return has been started, you can go back to the main page, and you will see beside the old return a garbage can; just click on the garbage can beside the return you want to delete. 

Thank you for choosing TurboTax.