A crab does not have the force or strength to fully pinch or cut your finger off but even then the crab can pinch your skin of your finger enough to cause some serious damage to where your finger could be almost cut off but the crab cannot cut through the bone or pinch through the bone.
So never pick up a crab or a lobster.
A lobster can nearly cut your finger off as well.
Yes a lobster does have the ability to take your finger off.
Lobsters are very strong and if you handle the lobster without gloves and the lobster can move it's arms and head around the lobster could use it's claws to pinch your finger and cut the finger off.
Lobsters are strong enough to take a kids or even adults finger off.
My brother once picked up a lobster when he was 18 while at a beach and the lobster did actually nearly severe his finger and thankfully he got emergency help.
The finger had to be sewn back on and he was in pain for quite awhile.
So never ever pick up a live lobster without gloves and you need gloves that cannot allow the lobsters claws to pinch through.
Or better yet avoid picking up the lobster when it's out in the wild.
Lobsters can do some serious damage when they want too so avoid touching them as they can and will harm you or take your fingers off.