Incest doesn’t cause mutations. The mutations are there anyway – everyone has some! Some mutations are recessive, that means they only cause an effect if you have two copies of them – one from your mother and one from your father.
Siblings who have a parent with a recessive mutation have a 50% chance of both having at least a single copy of the same mutation. If they had a child then there is a 25% chance of the child with double recessive mutations. This is much higher than in the general population. So harmful recessives are more likely to be active in the children.
This also happens if parents are less closely related (e.g. niece and uncle, second cousins) but the chances of the same harmful mutations coming from both parents are lower.
If this happens over multiple generations then the chances increase.
We actually do this deliberately with animals to increase the chance of beneficial recessive mutations reinforcing themselves, such as with pedigree dogs and cats. But this only works because the animals born with too many harmful mutations are killed.
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