There were a few ways in which you could kill your marapets. In which your marapet would die and go to the graveyard, and eventually turn to a zombie. But there is only one that works currently and that would be poison.
I never did that, because I never had the need to see my marapets as zombies. To buy the poison that will kill your marapet, you need to go to the poison shop in Eleka Castle's fountain.
To buy the poison you also need RP. To be able to earn RPs you need to do a lot of Leprechaun's Quests.
Marapets used to be arranged in a way that if you did not feed your pets they would eventually die and reach the graveyard. But not anymore. There is no telling when, or if that will work like that again.
If you have a gruesome mind maybe you want a headless pet FOR FREE, you can have a "fairy" the Decapitating Fairy turn your pet into "headless" by using a guillotine on them. What a fairy...
Alternately, there is also the choice of having your pet mummified, which is also a horrible gruesome death by the Sundial Fairy. If you are crazy enough to get it done you have to go to the Sundial with a mummy doll. Mummy dolls are not cheap, you need BPs to get them. If you want to accumulate BPs, you need to battle with your pets in the Battle Arena.