‘And Joseph took the body, and wrapped it in a clean linen cloth, and laid it in his own new tomb, which he had hewn out in the rock, and he rolled a great stone to the door of the tomb, and departed.'
Joseph (no doubt along with his servants) treated the body with all reverence. He wrapped it in a clean linen cloth and laid it in his own new tomb. Note again the stress on ‘clean' and ‘new'. His body was being treated as ‘holy' and as set apart to God. Then once this was done to his satisfaction Joseph had a great stone rolled across the entrance of the tomb, and returned home. He had paid his final respects to the One he had seen as a Prophet. So having died as One Who was ‘numbered with the transgressors' Jesus' holiness is now being brought out in his burial. All this would be done fairly rapidly so as not unnecessarily to infringe on the Sabbath. It was a generous gesture on Joseph's part, for the burial of a criminal in the tomb rendered it unusable by the family.
‘Which he had hewn out in a rock.' This is an unexpected detail in Matthew who tends rather to abbreviate, and may be intended to look back to ‘the rocks were rent' (Matthew 27:51). The idea might be that this tomb which was hewn out by man would also soon be ‘torn asunder' by God. It would not be able to hold Him.
The great stone may have been a boulder, but it was more likely a shaped stone in circular form like a wheel, which could be rolled across the entrance, for it would seem that the entrance to the tomb was relatively large (Peter only had to stoop to look in, not go down on his knees - John 20:5). Such stones were common in the case of expensive tombs.
It should possibly be noted that official mourning was not allowed for an executed criminal which helps to explain why there is no indication of it.