The mouth is synecdoche for the whole person. AT: "I will tell" or "I will speak with my mouth and tell" (See: [[rc://en/ta/man/translate/figs-synecdoche]])
This can be restated to remove the abstract noun "righteousness." AT: "how righteous you are" or "all the good things you do" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
The abstract noun "salvation" can be stated as an action. AT: "how you have saved me" or "how you save people" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
Possible meanings are 1) "I will tell them of the mighty deeds the Lord Yahweh has done" or 2) "because the Lord Yahweh has given me strength to do mighty acts."