According to Cassidy, this word, which means a disturbance or trouble, is derived from the Irish word maidhm, which means an outbreak. Sounds plausible enough when you first hear it but let’s examine the evidence carefully. First of all, what does the word maidhm mean?
Maidhm is pronounced similarly to the English word mime. It does mean an outbreak. It is used of something which has been held in and suddenly breaks through. So a maidhm shneachta is a maidhm of snow, an avalanche. A landslide is a maidhm thalún, while a maidhm phortaigh is a distinctly Irish natural disaster, the bogslide.
So, can maidhm be used for riot or civil disturbance? Irish is very rich in words and phrases for disturbances or hubbub. Trioblóid, ciréib, cíor thuathail, cath, ruaille-buaille, rí-rá, fuirse má rabhdaileam. Maidhm is not one that would normally be used. If someone said “Bhí maidhmeanna i mBéal Feirste aréir”, an Irish speaker would take this to mean that there were landslides of some kind in Belfast, not that there were riots.
When maidhm is used about warfare, it has a very specific meaning, namely that your defensive line has broken and that your troops are running away. In other words, it means a rout or catastrophic defeat. This is not at all what the word mayhem means, of course.
And in any case, the word mayhem doesn’t sound much like maidhm and it has an unassailable history going back to the 13th century, before any Irish ghettoes appeared in the English-speaking world. It derives from Norman French and is a legal term. Cassidy mentions the dictionary derivation but obviously prefers his own fantasy version to reality.