The costs were trimmed to the absolute minimum.

Literal

Costs [topic-は] at-the-limit [until-まで] were-cut-down.

ギリギリ is a mimetic adverb meaning 'barely, at the very limit.' 切り詰める means 'to trim, cut back.' The passive ~られた frames the cost-cutting as something done to the costs rather than by a specific agent.