Not mincing one's words
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The German equivalent of this expression developed from theatre. In German the saying "not taking a sheet of paper in front of your mouth" (Kein Blatt vor den Mund nehmen) means to speak up directly, to give your opinion.
In the past, the comedies in the theatre were quite unsparing - even high statesmen and politicians could be ridiculed and criticised. To prevent the actors from being punished for this, they hid their faces behind masks.
In the early days of theatre, however, masks did not yet exist and therefore actors simply used a sheet of paper.
So if you don't mince your words (or in German "you do not hold a sheet of paper in front of your mouth", you speak your mind without hesitation, you speak without embellishment or say something directly, even if it is unpleasant.