you can delete some types of orders .These types are -
Any order that does not meet one of the above criteria cannot be deleted.
Some other examples of where an order cannot be deleted would be in orders where payment has been processed through Shopify POS or a payment provider in the online checkout. These types of orders can be archived, but not deleted.
Also, just for some extra context, for apps like Edit Order which creates a new modified order to make those edits, you would not be able to delete the original order. However, you would be able to delete the edited order that would be created by the app.
WARNING: ACCORDING TO RULES YOU CAN NOT DELETE PAID ORDERS DATA FOR AUDIT PURPOSE (please i got this news before i don't know now what is the rule about deleting orders)
Thank you for reaching out. The information @msk has posted is correct, as per our page on deleting orders. I would recommend checking your new accounting software to see if you can filter our these older orders, otherwise yes, you would need to start a new Shopify store if you want these orders to not appear.
Victor | Shopify Social Care