Can Spark Shipping automatically remove products in my store?

Spark Shipping does not remove products from your store. 

With inventory automation, when a vendor sets a quantity of zero (i.e quantity=0) Spark Shipping will mark that product as a zer0  quantity (i.e . quantity= 0)

Your shopping cart then controls what happens next. From there you can set your shopping cart to show the item as out of stock, remove the product from your site, etc. 

Also see - How to automatically mark a product as out of stock when the vendor no longer carries this item