。
She cut her finger on a piece of broken glass.
Literal
She [topic-は] glass [of-の] fragment [with-で] finger [object-を] cut.
ガラス is the loanword for the material 'glass,' from Dutch glas via Edo-period trade — the same Dutch-via-Dejima route that brought コップ ('cup'). 破片 ('fragment, shard, splinter') is a Sino-Japanese compound: 破 ('break') + 片 ('piece'). The で here is the instrumental — 'with, by means of' — though the contextual sense is more 'on / against,' since the glass is the agent of cutting rather than a tool intentionally wielded. Japanese で comfortably covers both intentional instrument and incidental cause: 包丁で切る ('cut with a knife') and ガラスで切る ('cut on glass') share the same particle.