Can mini strokes lead to mental impairment or mental illness?

Yes. Stroke = neuronal damage or death. You lose brain cells, you lose function. The extent of functionality lost is hard to predict but naturally depends on the anatomic area affected by the strokes. Multi-infarct dementia is a form of progressive dementia caused by repeat stroke occurrences.

Related Questions

I heard mini strokes can lead to a massive stroke but do they cause mental impairment or mental illness?

Clarification. Let's call your "mini strokes", small lacunar infarcts, and thus, these would imply small subclincal injury. Multiple such events can result in dementia. True mental illness as treated by psychiatry is not due to stroke.