Did you mean just use edit action to change product's image to empty and delete the file without delete product?
if that's the case you could define a hidden input to store delete action
@Html.Hidden("deleteImage","false")
and define button as Delete Image
use javascript to set hidden input to true
<script>
function DeleteImage(){
$("#deleteImage").val('true');
}
</script>
and then when you click post to the Edit Action
public ActionResult Edit(Product product, HttpPostedFileBase file,bool deleteImage)
{
if (ModelState.IsValid)
{
if(deleteImage){
p.Image="";
}
}
}