“by the mercies of God”

Mercies is an interesting word in the Greek. It is the word οἰκτιρμός (G3628) oiktirmós; gen. oiktirmoú, masc. noun from oikteírō (G3627), to have compassion on. Pity, compassion, mercy, but referring to a feeling that is not as strong as éleos (G1656), mercy. Oiktirmós is the pity or compassion which one shows for the sufferings of others.[1]
οἰτιρμος is only used four other times in the new testament, and is translated as compassion (2), mercies (2), and mercy (1). These uses can be found in: Romans 12:1; 2 Corinthians 1:3; Philippians 2:1; Colossians 3:12; and Hebrews 10:28.
In 2 Corinthians 1:3 God is described as “the Father of mercies and God of all comfort”. The essence of Paul’s thought can be summarized thus: God comforts us in our troubles so that we in turn can comfort others in their troubles, exactly as God comforted us.[2] That is why God is described as “the Father of mercies”. In Romans 8:35 Paul asked the question, “Who will separate us from  the love of Christ?” then in verses 38 and 39 he answers his question in this way:
“For I am convinced that neither death, nor life, nor  angels, nor principalities, nor things present, nor things to come, nor powers, nor height, nor depth, nor any other created thing, will be able to separate us from  the love of God, which is in Christ Jesus our Lord. “
This best explains the mercy that God shows us on a daily basis. No matter what we face, no matter what we are going through God is there for us. So when Paul says “Therefore I urge you, brethren, by the mercies of God” in essence what he is saying is “because of all that God has done and is doing for you…”
[1] The Complete Word Study Dictionary New Testament
[2]Believer's Study Bible. 1997, c1995. C1991 Criswell Center for Biblical Studies. (electronic ed.) (2 Co 1:3). Nashville: Thomas Nelson.