On scholarly study of Basilides using Mark, first Roukema:
Another conception of Jesus' supposed death is given by Basilides of Alexandria. Irenaeus (Against Heresies i.24.4) transmits the tradition that in Basilides' view Jesus had not been crucified at all, since Simon of Cyrene had taken his place. Basilides apparently deduced this from the Gospel of Mark, which first introduces Simon of Cyrene and subsequently says that they brought 'him' to Golgotha and crucified 'him' there (Mark 15:21–24). The context shows that 'him' refers to Jesus, because previously it is written, 'Then they led him out to crucify him' (Mark 15:20), and this is unmistakably about Jesus.
But Kelhoffer points us in the direction of Basilides using a gospel harmony starting with Irenaeus's account:
He [Christ] appeared on earth as a man and performed miracles (apparuisse eum . . . virtutes perfecisse). Thus, he himself did not suffer. Rather, a certain Simon of Cyrene was compelled (Simonem quendam Cyrenaeum angariatum) to carry and erroneously crucified (et hunc . . . crucifixum), being transfigured by him ... [Jesus], so that (ut) he [Simon] might be thought to be Jesus. Moreover, Jesus assumed the form of Simon and stood by laughing at them.
Grant identifies the laughing to come from Psalm 2 but Kelhoffer goes on to note:
Apud Irenaeus, Basilides's Docetic christology appears to be based upon a conflation of material preserved in Mark 15:21" and the Matthean parallel." Mark has the (historic) present active indicative (ἀγγαρεύουσιν), which Matthew changed to the aorist (ἠγγάρευσαν). At the very least, the perfect passive participle reflected by Irenaeus (angariatus) stems from Irenaeus's use of Matthew and-or Mark or, perhaps, from a harmonized version of this gospel material.
Of course Basilides used a 'harmony.' The canonical texts are stacked in a manner that won't allow the substitution narrative to make sense. Even the Arabic Diatessaron doesn't work:
And the Jews took Jesus, and went away to crucify him. And when he bare his cross and went out, they stripped him of those purple and scarlet garments which he had on, and put on him his own garments. And while they were going with him, they found a man, a Cyrenian, coming from the country, named Simon, the father of Alexander and Rufus: and they compelled this man to bear the cross of Jesus. And they took the cross and laid it upon him, that he might bear it, and come after Jesus; and Jesus went, and his cross behind him.
19 And there followed him much people, and women which were lamenting and raving. But Jesus turned unto them and said, Daughters of Jerusalem, weep not for me: weep for yourselves, and for your children. Days are coming, when they shall say, Blessed are the barren, and the womb's that bare not, and the breasts that gave not suck. Then shall they begin to say to the mountains, Fall on us; and to the hills, Cover us. For if they do so in the green tree, what shall be in the dry?
24 And they brought with Jesus two others of the malefactors, to be put to death.
25 And when they came unto a certain place called The skull, and called in the Hebrew Golgotha, they crucified him there: they crucified with him these two malefactors, one on his right, and the other on his left. And the scripture was Arabic, fulfilled, which saith, He was numbered with the transgressors. And they gave him to drink wine and myrrh, and vinegar which had been mixed with the myrrh; and he tasted, and would not drink; and he received it not.
28 And the soldiers, when they had crucified Jesus, took his garments, and cast lots for them in four parts, to every party of the soldiers a part; and his tunic was without sewing, from the top woven throughout. And they said one to another, Let us not rend it, but cast lots for it, whose it shall be: and the scripture was fulfilled, which saith, They divided my garments among them, And cast the lot for my vesture.
30, This the soldiers did. And they sat and guarded him there. And Pilate wrote on a tablet the cause of his death, and put it on the wood of the cross above his head. And there was written upon it thus: THIS IS JESUS THE NAZARENE THE NAZARENE, THE KING OF THE Jews. And this tablet read many of the Jews: for the place where Jesus was crucified was near the city: and it was written in Hebrew and Greek and Latin. And the chief priests said unto Pilate, Write not, The King of the Jews; but, He it is that said, I am the King of the Jews. Pilate said unto them, What hath been written hath been written.
“Finally, from so little sleeping and so much reading, his brain dried up and he went completely out of his mind.”
― Miguel de Cervantes Saavedra, Don Quixote