rule to remove items from Shopping cart
I have created a rule that empty cart before adding any new item. So the only latest item will be in the cart. I think thats what you need to do. Any other conditions can be added one by one.

If you want to clear cart totally then you can use after adding product event

{ "rules_empty_cart_" : {
    "LABEL" : "Empty cart ",
    "PLUGIN" : "reaction rule",
    "OWNER" : "rules",
    "REQUIRES" : [ "commerce_cart", "rules" ],
    "ON" : { "commerce_cart_product_prepare" : [] },
    "DO" : [
      { "commerce_cart_empty" : { "commerce_order" : [ "commerce_order" ] } },
      { "drupal_message" : { "message" : "Cart empty event executed.!!" } }
    ]
  }
}


Hope it will help!