Yes you can take the mold off the part of the bread that is moldy and still eat the rest of the bread.
Whenever I have bread that has started to mold I tear off the moldy parts and throw them outside for the birds or other animals to eat and then I eat the rest of the bread.
If the mold hasn't grown on all the bread and only part of the bread then the rest of the bread is still okay to eat as long as you just remove the moldy part of the bread first.
If you notice mold growing in a loaf of bread or on some bread remove the moldy parts to keep the rest of the bread from getting moldy as quick.