A nozir is forbidden grape products, haircutting and to become tomei from a dead body. After successful conclusion of his nezirus, he goes through a process ending with the waving of his korban as described in Bamidbor 6 (20)
The kohen shall wave them as a waving before the Lord; it is consecrated to the kohen, along with the breast of the waving and the thigh of the uplifting. After this, the nazirite may drink wine.
The Torah mentions the release of only one of the prohibitions “ After this, the nazirite may drink wine.”
In the mishnah in Nozir 6 (9) the Tanna mentions the release of two prohibitions and says
Afterward, the nazir is allowed to drink wine and become impure through contact with the dead.
The Torah only speaks about drinking wine; the mishnah includes becoming impure through contact with the dead; neither mentions the permission to shave his head (after his hair has regrown). Why?