Andrew Murray emphasizes the profound meaning of taking up the cross as a call to self-denial and surrender to Christ. He explains that the disciples initially struggled to understand this concept, but it ultimately signifies recognizing the death sentence on our sinful nature and the necessity of crucifying our flesh. Murray highlights that true fellowship with Christ involves living in the awareness of our crucifixion with Him, as expressed by Paul in his letters. He encourages believers to seek daily communion with the crucified and living Lord, understanding that the power of the cross is not just for salvation but for ongoing spiritual fellowship. The sermon calls for a deeper engagement with the cross, leading to transformation and a life that glorifies Christ.