Exorcistic material is actually very common in Mesopotamia. The method and recipient of such magical actions changed over time, transitioning from mostly natural adversaries (snakes, scorpions, etc) to phantoms and spirits (the alû, gallû, lilû, etc).
Traditionally, invasive and oppressive entities acted in Mesopotamia through the use of sickness. A majority of the material available to us comes in the form of workbooks, with a "diagnostic" section followed by a "treatment" section, meant to help the specialist (called an āšipu / āšiptu) determine what entity had attached itself to the patient and by what means it could be removed.
There are a handful of academic studies of these tablets. The most thorough of which are:
• Corpus of Mesopotamian Anti-Witchcraft Rituals
• The Maqlû Series
• Šurpu: A Collection of Sumerian and Akkadian Incantations
The Corpus of Anti-Witchraft Rituals is unreasonably expensive on Amazon, so I've provided a PDF of it. The Šurpu collection is unavailable on Amazon, so I've provided a PDF of it. The Maqlû Series is available and affordable on Amazon, so please consider buying it if you have a serious interest in this kind of magic.