How to open a malfunctioning tamper-proof bottle cap? I have a bottle of oil I want to open. It is a glass bottle with a threaded metal cap. It is the type of cap which is connected in a few places to a lower ring. Usually, one just unscrews the cap, and it tears off the ring, which stays below the threads.
I now have a bottle whose cap+ring system is too loose. When I turn the cap, the whole thing, cap+ring, rotates freely without unscrewing or exerting a tearing force on the connection places.
What I tried, unsuccessfully:

turn it vigorously
grip it with a towel while turning
exert an upward pull while turning it
holding the lower ring with the fingers of one hand while gripping the cap with the fingers of the other hand through a towel, and exerting force in opposite directions
trying to cut the connection places with a knife tip (doesn't get cut, but it feels like the knife might slip and hurt me any time).

Note that this is a different problem than the much more common one of both not turning and my fingers slipping on the cap instead. I can grip the cap perfectly well, and it rotates very easily, it just doesn't unscrew or separate from the ring.
I've had this before, and solved it by breaking the join  between cap and ring with a small screwdriver, one section at a time.  Long nose pliers may be handy towards the end.  You might manage to get the tip of a butter knife in the join instead of the screwdriver.
Trying too hard when it's not coming off tends to deform the threads in the cap, so it may not go back on securely later - you might need to decant the contents.