To disable the common thank-you email message that gets sent for each order, regardless of item(s) ordered, go to Seller Admin > Account Preferences > Common Thank-you Email, delete the message template there, and click Submit to save changes.
To disable the product-specific thank-you email for digital products (such as a Download or Send Codes), to to Seller Admin > View/Edit/Delete Products, select a product and click Edit, tick the box to Enable Templated Email and leave the Email Message field blank (our system can't generate a message from a template if there's no template given :^), then click Next until you can Submit settings.