Does a divorce take effect when a husband says to his wife: "You are divorced from my responsibility" if she takes her belongings, knowing that she did take them, and a divorce has previously occurred between them once?

If, by that phrase, you intended to effect a divorce if the wife took her belongings, and that happened, then a single divorce has occurred. And if you had divorced her once before that, then this is the second divorce, and you can take her back before her waiting period (iddah) ends. However, if you intended it as a promise of divorce, then no divorce occurs when she takes her belongings, and you are required to offer an expiation for breaking an oath.