You ran out of something.
Is 切れる right and can you also use 無くなる? To say that something is in low supply or almost finished?
And in what situation would you use which?
-I ran out of tape/tissue
-my phone battery died
は 日本語 で何と言いますか？

質問を翻訳

It depends on the importance of what you (will) run out of.

切れる means "be cut" here, in a sense of 'Replenishment that should be done continuously will "cut"/blocked'. So this expression/word 切れる implies the need strongly for replenishment before consuming it completely.
On the other hand, 無くなる means simply "ran out" and it doesn't have such a (serious) nuance.

-I ran out of tape/tissue -- 無くなる
-my phone battery died -- 切れる

-When running out the Fuel on cars that crossing the vast desert. -- 切れる
-When running out the Fuel on cars which using for commuting in town every day. -- 無くなる