The British Army fighting the tribal insurrections on the tribal NWFP (North West Frontier Province) of India in the mid 1890s learned of the potential hazards of this practice. Issued with the then new Lee-Metford rifle in .303 shooting heavy RNFMJ bullets, they too often failed to stop highly determined tribesmen in the charge. There were recorded cases of men hit three to six times still reaching the British lines and running amok with various nasty bladed weapons. (Same issue as US forces in the Philippines with the .30 Krag against Moro tribesmen.)
Many troopers filed the jacket nose off to improve the bullet's terminal effectiveness. However, cores blown out and jackets left in the bore occurred. The temporary answer was the expanding bullet developed and made by the Indian Dum Dum Arsenal, hence the name for expanding bullets in common parlance, followed by a series of three hollow-tip models developed at Woolwich Arsenal in the UK.
Many years ago, I had a 303 MK VII (Spitzer FMJ) bullet jacket fail on me in a Ross rifle. The front-end of the jacket apparently split as the bullet entered the rifling leaving a near perfect copper alloy tube stuck just ahead of the chamber. The core of course went somewhere down range. Luckily, enough jacket stuck out into the chamber to stop another cartridge being chambered. Brig. Gen. Julian Hacker mentions 150gn FMJ bullet jacket failures as common too with early production lots of the original .30-06 round and many M1903s ended up with several inches of thin tube swaged into the rifling and rolled several inches long by the passage of subsequent bullets. Apparently and surprisingly, Hacker reported no great increase in pressure, but doesn't comment on how well such rifles shot after such treatment.
So sure, cut the tips of your FMJBTs, but be aware that there are risks involved.