Is it true that I cannot buy a puppy and smash it deliberately for my
perverse amusement (regardless of whether it's in front of them or
not)? If I cannot, can you point me to the relevant laws?
Is it true that I cannot buy a cow or a pig and throw it into a
woodchipper similarly for my perverse amusement? If I cannot, can you
point me to the relevant laws?
You can't do either of these things. Every state has some sort of law banning cruelty to animals.
For example, in Colorado, the laws prohibiting cruelty to animals are codified at Sections 18-9-201 to 18-9-209, Colorado Revised Statutes. The core language of the statute is codified at Section 18-9-202(1)-(1.5) (as of July 1, 2014) which states (in language that is not atypical nationally) that:
(1)(a) A person commits cruelty to animals if he or she knowingly,
recklessly, or with criminal negligence ovedrives, overloads,
overworks, torments, deprives of necessary sustenance, unnecessarily
or cruelly beats, allows to be housed in a manner that results in
chronic or repeated serious physical harm, carries or confines in or
upon any vehicles in a cruel or reckless manner, engages in a sexual
act with an animal, or otherwise mistreats or neglects any animal, or
causes or procures it to be done, or having the charge or custody or
ay animal, fails to provide it with proper food, drink or protection
from weather consistent with the species, breed, and type of animal
involved, or abandons an animal.
(1)(b) Any person who intentionally abandons a dog or cat commits the
offense of cruelty to animals.
(1.5)(a) A person who commits cruelty to animals if he or she
recklessly or with criminal negligence tortures, needlessly mutilates,
or needlessly kills an animal.
(1.5)(b) A person commits aggravated cruelty to animals if he or she
knowingly tortures, needlessly mutilates, or needlessly kills an
(1.5)(c) A person commits cruelty to a service animal if he or she
violates the provisions of subsection (1) of this section with respect
to a service animal . . . whether the service animal is on duty or not
The rest of the statute mostly spells out sentences and other remedies and definitions applicable to these offenses. For what it is worth, the laws against cruelty to animals, and the now obsolete laws prohibiting cruelty to slaves that existed when slavery was legal in the U.S., were quite similar.
So, yes, an animal (pet or otherwise, there is almost no formal legal distinction between pets and non-pets, even though in practice, people evaluate what is cruel to a pet and to a farm animal differently) is property. Yes, someone who owns an animal may intentionally kill it or maim it, or have someone acting at the owner's instructions do so.
But, an owner must do so humanely under the circumstances and must do so for a good reason (such as for food, to put down a sick or injured or dangerous animal, or for experimental research).
Ranking states is a bit difficult. There are some states that have felony cruelty to animals statutes and some that don't. I don't have the time to look for an exhaustive survey of the law state by state (one summary is here). There are some states that are quite specific (like Colorado) and others that are more general in language. Idaho has an express provision that killing animals that are harrying livestock is an acceptable reason. Some of the difference boils down to how the law is applied in practice, rather than to the language of the statutes on the books.
The overall gist of the statutes, however, is pretty similar: don't be cruel in how you do it, and don't harm animals if you don't have a good reason for doing so.
There is also a lot of conduct (for example, separating mothers and young children, amputating body parts such as claws or tails or reproductive organs without consent, or confining and leashing them) that would cause emotional harm to animals and which would be grave human rights abuses, that is not prohibited as cruelty to animals.
Similarly, there are many farming practices that are accepted as not violating these laws like the process of creating veal or foie gras that could be characterized as cruel but are accepted as not violating the laws against cruelty to animals.
To a great extent, these exceptions, which are rarely codified, are simply a matter of custom and practice and tradition, rather than having any well reasoned logical derivation from statutory language.