The idea of service and Jesus giving his life as ransom is solidly connected if we remember that Mark 10:35–45 is a unity of events and instruction.
Jesus spoke first of all with the sons of Zebedee about his bitter cup, his suffering, and death. Then he spoke with the twelve about the necessity of service. In Mark 10:45b everything is drawn together: Jesus’ service is a service wherein he drinks the cup that God gives him and undergoes the baptism by immersion that awaits him. For he has come to serve, and that is in his case especially: to give his life as a ransom for many!
One could see a certain connection with Isaiah 53:10: The servant of the Lord [servant!] who shall make his life an offering for sin. This could be a way to see the link between service (Mark 10:45a) and ransom-price (Mark 10:45b). The prophecy of Isaiah 53:1–12 is certainly connected to the words of Jesus, but we could ask if guilt offering (’asjam) of Isaiah 53:10 is the same as ransom (the Greek word lutron is in the Greek translation of the Old Testament never a translation as ’asjam). It is also to be noticed that the expression Son of Man
does not run parallel with Isaiah 53:1–12 as prophecy of the servant of the Lord.1
Barrett2 starts exactly from the other side: the title Son of Man
causes him to look for the background of Mark 10:45 first of all to Daniel: the suffering of the individual believer becomes a substitute for the people as a whole.
Attention for the prophecies in the background must not result, however, in losing sight of the foreground. These words about service and ransom have their connection also without quoting prophecy. Jesus calls himself the Son of Man because he is going to speak about the task for which he came
(on earth, becoming man). He points to the serving character of that task because of the wrong attitude of the twelve. And he focuses everything on his death because the disciples quarrel about the glorification and constantly ignore the way of suffering and death. Jesus typifies his dying finally as a ransom for many in order to show that his death will take place in the service of others. He is the dying Servant: this is the ultimate message for the twelve!3
45 For even the Son of Man came not to be served but to serve, and to give his life as a ransom for many.”