My daughter had a terrible time getting rid of her "Buddy"...she had 5 or 6 and loved to play with them just like toys, then suck on them for naps & bedtime. I tried the cutting thing, but that didn't work for my daughter because she liked to play with them, too.
One day after some of them had been 'lost' somewhere in the house, she was down to one Buddy...and a man named Mike came to our house to tow my car to the repair shop after it had been hit on the street. Mike was talking to my daughter while I was signing some paperwork and he asked her about her Buddy. He said he didn't have one and 'can I have it?' and shockingly enough, she said yes and gave it to him. He left with the car (he secretly gave me back the Buddy) and the Buddy and when it came time for bed that night, she asked for it and I told her that she gave it to Mike and that he was gone now with the Buddy...she cried a little bit, watched a video and fell asleep while I was holding and rocking her, and that was it. She knows that Buddy lives with Mike, but we just don't know where that is! She would sleep with a stuffed 101 Dalmations dog and several Beanie Babies...we just filled up her bed with sleeping and playing friends just like Buddy had been, only now Buddy was helping someone else sleep because she didn't need him and he's happy with Mike! It's all in the presentation! We all laugh at that story now! BTW, she's 15 now and STILL sleeps with Lucky the dalmation! My son was much the same way...we 'lost' his one day and we all made a big deal about looking for it, and my son went to bed with his little blanket instead of Buddy and he was fine with it. He never asked for it again and slept with the little blanket ever since! Sometimes it's just a matter of transferring to something else. My son still has the little blanket on his bed...he's 10...but he doesn't have to have it to sleep, and he doesn't take it anywhere...it's just there and looks cute.
Good Luck!
S.