Where do I buy greater genetic mutators? I'm sure this is a silly question, but I've checked the shops several times and couldn't find it. Or is it obtained another way?

-> Shops tab

-> select Diamond Shop; scroll down to the "Diamond Shop" section

-> select the Mutators, Dyes & Disruptors tab

-> Greater Genetic Mutator (page 1)

there is also an item called a "Lesser Genetic Mutator" which will add a random carried trait to a tamed pet.
they can be bought with scales, earned through nurturing pets.

Shops > Scale Shop > Lesser Genetic Mutator (1,500 scales)

To add to what YureiNeko said, a Lesser Genetic Mutator also has the possibility of adding a random visible trait, not just a random carried.

This is a pet I added a LGM to, and it gave it a visible rather than a carried;
https://www.sylestia.com/view/pets/?petid=8236892

For reference, this is GGM description:


To help you out a bit, I went ahead and sent you 3 GGMs.

Wow, thank you! This is really generous! :D

The diamond shop is the only one I didn't check haha. Thanks all!

I'm going to add on a bit to what has already been said, there is also the option of going to the trade broker(Trade>Trade Broker) and then picking "Genetic Mutator" for the type. This method tends to be more pricey as you would be buying from other players but it allows you to buy with gold whereas buying from the Diamond Shop you'd have to use Diamonds and buying a lessor from the Scale Shop requires you to use scales.