Both of these phenomena are similar but there is a slight difference between the two. Let’s look at some definitions (both from dictionary.cambridge.org):
dehiscence – the splitting or bursting open of a pod or wound
evisceration – to remove one or all of the organs from the inside of a body
In medicine, dehiscence (when a wound dehisces) is generally used when a wound or surgical incision ruptures. This could be due to physical stresses on the wound (movement, insufficient undermining, etc.) or due to infection. This is one of the reasons why patients should avoid excessive movements that affect the wound or heavy lifting.
Evisceration is the removal of one or more organs from the body, either by accident or on purpose. Accidents in an industrial workplace can lead to accidental evisceration whereas some forms of torture, execution, and suicide can also be causes considered “on purpose”. Generally in the medical world, evisceration happens through a horizontal incision in the abdominal region. The intestines can also be eviscerated through the anus, although this is not a common phenomenon. Survivors usually have to take special nutritional measures (such as parenteral nutrition – through an IV) due to the lack of part or all of the intestine.
From a language point of view (since you posted in the English grammar section of Quora), both words are nouns and are found most commonly in the field of medicine. These words are generally not used in everyday speech as they have a high register.
Using the International Phonetic Alphabet (IPA), dehiscence is often pronounced as /dɪˈhɪsəns/ and for evisceration, it’s /ɪˈvɪsəˌɹeɪʃən/.