Wash and pat dry the oxtail pieces. Season with salt and pepper.
Add olive oil to the Instant Pot and turn on saute mode. When hot, add the oxtail and brown on all sides. Remove from the pot.
Add the onion, celery, and carrot. Saute for 3 minutes. Turn off saute mode. Add the garlic, thyme and rosemary. After 1 minute, pour in the beef stock and red wine and whisk to remove the browned bits from the bottom of the pot. Add the tomato puree and stir well. Add back in the oxtail.
Lock the Instant Pot lid and set the vent to sealing. Set to pressure cook for 45 minutes. When finished, allow a natural release of pressure (about 15 minutes).
Remove the oxtail from the Instant Pot. Remove any excess fat or grease from the cooking liquid.
Shred the meat away from the bones. Discard the bones and connective tissue. Return the meat back to the Instant Pot with the sauce. Stir it all together.
If it’s not thick enough, turn on saute mode again and cook down until thickened.