Been there and done this before.Take the die out of your press and put the case in the shellholder. Ram it all the way up so that it's sticking out of the top of the press, then firmly clamp the bullet with a pair of Vice Grips. Lower the ram. You won't save the bullet this way but unless you rip the rim off the case you will save it.
The technique I use with a kinetic bullet puller is to hold it loosely between thumb and forefinger and bring it down swiftly on the end grain of a short piece of 4x4. Holding is loosely allows it to rebound without resistance, nearly doubling the extraction power.
I am told RCBS recommends striking a harder surface (concrete, I am told). But wood has always worked for me.
I first used the loose grip to prevent bending of the aluminum handle shaft (my RCBS bullet puller is a 30 year old model), but soon discovered that it made pulling the bullets more efficient and effective.
Just my experience.
Lost Sheep
Post a picture of this stubborn cartridge if you can get it focused close enough, please.I'm experimenting with a newly purchased press and seated a bullet WAY too far. A bullet puller won't budge it. How do I get this cartridge apart aside from cutting it...which could create it's own issues?
Never in my life have I needed 10-15 hits to pull any pistol or larger rifle bullet.
...
Like everyone else is saying.
Hit the puller on a hard surface, and hit it like you mean it!
It will come out.