1.The expression means to give yourself away.
2. This means waiting.
3.I mean to do that.
My question is " to give" should be corrected into giving.Am I right?Thanks!
No, it's fine to me, but I would italicise it:
This expression mean to give yourself away.
2 = This involves waiting
3 = I intend to do that
Where mean is similar to involve, then it's right to use a gerund. The first is different; it is giving a definition, which is why I put it in italics, to separate it from the rest- as a definition, it follows different rules and we normally use an infinitive for a definition.