1) Reheat the knife, and try again
2) Have a rubber band handy to create a tourniquet
- When it scabs over, you can remove the tourniquet
3) Have some quickstop powder, or cornstarch ready like Threehorses mentioned
I don't know how good their circulation is in their foot, but it's unlikely that he would bleed enough through his toe to kill him. This is mainly because there are no major arteries that far down. Also, there's so little good tissue left there that the distal part of his toe has very little circulation anyway.
If it just hanging on by a bit of flesh it should be pretty easy. Sounds horrible but unless you have a medical scalpel a sharp sterilized pair of scissors will do. Soak the foot in the mixture of betadine and water to kill the germs and them amputate. If it bleeds let it for a bit to 'rinse' the infection out. Use blood stop powder or gentle pressure with your hand and a material that is non stick so you don't pull out any clots. Cover with neosporin and bandage. Change bandage every day until it is healed. Keep him by himself so he can rest. DO NOT use betadine after this. Yes it kills germs but it also kills the new tissue that is trying to grow to heal the foot.