You think you can put the answer into a box and call it property and you have solved something. Beyond the right to dispose of property is the moral fight of affecting hearts and minds... Encouraging all you know, for example, to not buy pet food with unidentified "animal products" in them, for example. If it says "chicken", Beef" etc on the label then that is what it is... If it says "animal byproducts" or "Animal bone meal" it is horses. (even check your horse food folks, you'll be surprised). There are a lot of foods out there containing no unidentified meat products, just have to shop at stores and buy good foods other than the cheapest brands.
It is perfectly right for a person who owns property to dispose of it however he sees fit. It may be heartless, unwise, unloyal and poor stewardship but those issues are between the property owner and God. If it's his property what right do I have to interfere?
Rest assured that I would never mistreat my animals (we used to have cats but had to find them new homes when the baby came (allergies don't you know). We treated them like kings and queens and found them very good homes). I try to practice proper stewardship of the goods entrusted to me and that stewardship demands that my property is treated well.
That being said I find nothing in the Bible or the Constitution that lets me dictate to my fellow man how he should treat his property.