Luke 8:39: "'Return to your home, and declare how much God has done for you.' And he [the formerly demon-possessed man] went away, proclaiming throughout the whole city how much Jesus had done for him."
Colossians 3:17: "And whatever you do, in word or deed, do everything in the name of the Lord Jesus, giving thanks to God the Father through him."
Numbers 6:26: "the LORD lift up his countenance upon you and give you peace."
1 Corinthians 10:16: "The cup of blessing that we bless, is it not a participation in the blood of Christ? The bread that we break, is it not a participation in the body of Christ?"
+++
"God's blessing" in the first few lines ("Sent forth by God's blessing, / Our true faith confessing, / The people of God from His dwelling take leave") seems to refer to Numbers 6:26. The situation the hymn describes is the same as what's in Luke 8:39.
Colossians 3:17 appears at the beginning and end of the second verse ("With praise and thanksgiving / To God ever-living, / The tasks of our ev'ryday life we will face" and "Then may all the living / With praise and thanksgiving / Give honor to Christ and His name that we bear").
1 Corinthians 10:16 seems to appear in the line "With Your feast You feed us" in the second verse. Shortly after this is the line "Unite us as one in this life that we share," which bears some resemblance to 1 Corinthians 10:17: "Because there is one bread, we who are many are one body, for we all partake of the one bread."
