There are several ways to remove items from Shopify using the Hyperspace integration.
You can disable a product that is checked SELL ON WEB using the DISABLE checkbox in Hyperspace. This is located next to each product in the INVENTORY tab in Hyperspace. The product will still remain in Shopify but it will not appear online to your customers. This does not delete the product from the Shopify admin. The DISABLE button will only hide it so it does not appear online to your customers.
Note: Be sure to leave the SELL ON WEB checkbox checked. If it is unchecked, this will break the connection to sync and Hyperspace cannot tell Shopify to disable the product.
Deleting Archived Products from Shopify
You cannot delete products in Lightspeed, you can only archive products in Lightspeed. When you archive a lot of products to clean out Lightspeed, Hyperspace has a function that you can run that will automatically remove all of the archived products from Hyperspace and Shopify. This process will delete the products from your Shopify Admin. At the bottom of the Inventory tab in Hyperspace you can click 'Remove Archived Products'.
Deleting Products from Shopify without Archiving
You can delete products directly from Shopify if you want. If you do this, be sure to uncheck the SELL ON WEB button in Hyperspace for products that you delete. If you do not uncheck this button, the product you delete from Shopify will come back.
Disable Checkbox in Lightspeed
Hyperspace will be adding a new feature so you can create a custom field in Lightspeed called: DISABLE. Checking this box will automatically click the DISABLE button in Hyperspace. This feature will be released on 11/01/2018.