English (1) Time is up !

When "up" is an adverb, it means
(1) 上
(2) 向上
(3) 到
(4) 一直
(5) 迄
(6) 及至
(7) 向上地

When "up" is a preposition, it means
(1) 截至
(2) 截
(3) 臨到

Here, "up" is a preposition (介詞/前置詞), it means "到了", so "time is up" means "時間到了".

As I know, "up" here means "previous" i.e. Time has already passed.