No, seriously now. They neuter thousands upon thousands of dogs and cats… Is there some big landfill of cat nuts somewhere?
Do they fry them up like the rocky mountain oysters?
[Just worried about where the rest of my cat ended up…]
“goolies” 
Love that word! I haven’t heard it for years.
I assume for male cats and dogs they perform something like a vascectomy not a castration. Similarly when neutering femal pets, I’d think it wouldn’t be a hysterectomy they were performing but somethign more like a tube tying. In this case there’s be little to dispose of.
They just ball 'em up and throw 'em away.
You’d be wrong. Spaying is the complete removal of the animal’s uterus and ovaries. Neutering is the complete removal of both animal’s testes. Presumably these are disposed of in the same manner as any other biological waste: sealed in specially marked containers (usually plastic bags for small quantities of material) and picked up by a medical waste disposal service.
Goolies is a very British term for the testicles.
Also ‘knackers’ or ‘cobblers’.
Wrong. One of the major benefits of getting 'em fixed is that they don’t do things like go loudly into heat (ever hear a Siamese?).
Animal chunks aren’t typically considered biohazard materials, since there’s not really that much humans can catch from dog and cat organs. As such, when we take something out that we don’t need for other purposes (sending off for histopath, saving for catfish bait, educational dissection, whatever) we just drop it in the OR trashcan. The trash gets taken out at the end of every surgery, or every surgery day, and bits and pieces go into the landfill just like that leftover chicken you cleaned out of the fridge.
Goolies. It’s what’s for dinner.
Naw - you take the whole thing out because you want to remove the hormones as well. Unneutered male cats and dogs are far more aggressive, and the cats are more inclined to spray. At the vet clinic I worked at, they went in the trash. It was always rather alarming to take out the trash when there was a big pair of dog nuts sitting on top, but there you go.
I think that’s what they call Swedish Meatballs
In my H.S. freshmen bio class, our teacher had her dog fixed and brought the testies in so that we could disect them. I’m usually not bothered by that sort of thing, but the “ewww yuck” factor really got to me that time for some reason. Maybe I was feeling some instinctual male sympathy for the dog.
Judging by the responses, disposal must vary by clinic. The small animal practice I work at has the spare bits rendered along with any dead bodies (hopefully not the same cat).
If there’s variation, then it must not matter exactly how bits are disposed of.
Just adding my 2 cents to get the most out of my temporary membership 
And if you feel guilty afterwards, there’s always Neuticles.
I went with a friend to get her Pomeranian neutered and the doc was kind enough to fish the 'nads out the trash or whatever to show us.
They were HUGE compared to what I expected! Either they’re like iceburgs, and most of 'em are below the surface, or the doc brought the wrong ones out.
Like everyone else has said, it is basically castation. In fact, a quick and easy way to see if a male dog has been neutered it to look at it from behind. Once, you’ve seen an unnuetered dog from behind, there won’t be any question at all as to if it’s actually castration or not.
I likes my dogs streamlined.
Our vet clinic put them in a plastic bag and popped them in the chest freezer. Our cremation service would take them (and any other various bits removed during surgeries) every couple of months and incinerate them free of charge.
Of course, this is after we would throw them at each other.
Did you know that cat nards are quite sticky?