。
She was fired for negligence.
Literal
She [topic-は] negligence [called-という] reason [by-で] was-dismissed.
という理由で is the standard frame 'on the grounds of X / for the reason X / on the basis that X' — packages a noun (or full clause) as a justification. The で here is the cause/grounds particle ('on grounds of'). 解雇する is the formal verb for 'dismiss / fire from a job,' contrasting with the more colloquial idiom クビにする ('fire,' lit. 'make into a neck'). The passive 解雇された ('was dismissed') is in keeping with the formal register.