The New Testament is filled with "take up your cross" Scriptures:
Matthew 10:38 Whoever does not take up their cross and follow me is not worthy of me. Matthew 16:24 Then Jesus said to his disciples, “Whoever wants to be my disciple must deny themselves and take up their cross and follow me.
Mark 8:34 Then he called the crowd to him along with his disciples and said: “Whoever wants to be my disciple must deny themselves and take up their cross and follow me.
Luke 9:23 Then he said to them all: “Whoever wants to be my disciple must deny themselves and take up their cross daily and follow me.
We often think of taking up our cross as dying to flesh, but Christ died to the his flesh in the garden when He said "not my will, but your will be done." Not that there was not some more 'dying to will' done as He carried the cross to Calvary, but that was not the primary reason He took up the cross.
Christ took up the Cross for every sinner. He carried it for our sake, not His. He wasn't paying a price for himself, but "He became sin who knew no sin that we might become His righteousness" We follow Him because of the price He paid for us. We follow Him because He laid down His life for us. We follow Him, because He was the only one that could bridge the gap between us and God.
Christ is not calling us to take up our Cross for our sake. Yes, it is a further process of dying to self, because we have to deny ourselves. The cross we carry is not for us. It is for the sake of those who we come in contact with daily. We are to take up the Cross and follow Christ in laying down our lives in service to others. We are to be His hands and feet bridging the gap between the lost and God.
It is our cross, because there are people in our sphere of influence that will only be reached for the Kingdom if we lay down our lives in service. There are people that will only be saved when we take up the cross and bridge that gap for them to see.