All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
"Mutilation" is the severing of the nose, ear, hand, or lip. The Hadeeth means that the animal is born complete, free from being severed, and if left alone, it will remain free from flaws unless people interfere and sever some of its body parts and as a result it becomes flawed. Likewise the child; he is born according to the Fitrah and if he is left untainted by external influences, he will be spared of flaws; however, his parents interfere and make disbelief attractive to him and force him into it. If he were left with his untainted innate nature, he would be free of disbelief, as he is born with a natural disposition towards faith and submission (to Allaah), but his parents turn him towards Judaism, Christianity or Magianism.
What you mentioned that some animals are born with deformities does not contradict the Hadeeth because the intended meaning of the Hadeeth refers to the great majority of animals which are born free of deformity. A few rare cases do not change this fact. Examples are used for the purpose of clarification and not limitation, suggesting that no animal would ever be born deformed. Moreover, the deformity could be the result of an illness that befalls the fetus or the mother and not related to its original state of creation.
Ibn ‘Aashoor commenting on the verse that reads (what means): {… and (Allaah) formed you and perfected your forms…} [Quran 40:64] said: "They (humans) were created in the best stature, as the form of man is a fulfillment of beauty, it is symmetrical in it. It is not flawed by the reprensibleness of one of its parts or the incompleteness of the usefulness of it that decreases the beauties of the rest of it; by contrast with most beautiful animals, birds, and fish, which walk on four with their heads often down, or crawl, or jump. Physical defects in man are caused only by external influences during the pregnancy period such as a shock to the mother's belly or an illness that afflicts the mother or the fetus during the pregnancy or afterwards. All this may cause deformation to the perfect physical form of man. This deformation is due to external effects and not related to the initial form created by Allaah. Rare as the deformation caused to the external mould of man is, it is not labelled as ugliness, but rather, it is relative deficiency in the perfect beauty of the human body." [At-Tahreer wat-Tanweer]
Allaah Knows best.