Does the Bible say do not mark your body?

Ye shall not make any cuttings in your flesh for the dead, nor print any marks upon you: I am the LORD. (Leviticus 19:28 KJV)

You shall not make any cuttings in your flesh for the dead, nor tattoo any marks on you. I am Yahweh. (Leviticus 19:28 WEB)

And a cutting for the soul ye do not put in your flesh; and a writing, a cross-mark, ye do not put on you; I [am] Jehovah. (Leviticus 19:28 YLT)

Adam Clarke’s Commentary

Verse 28.   Any cuttings in your flesh for the dead] That the ancients were very violent in their grief, tearing the hair and face, beating the breast, &c., is well known.  Virgil represents the sister of Dido “tearing her face with her nails, and beating her breast with her fists.”   

“Unguibus ora soror foedans, et pectora pugnis.”

                        AEn., l. iv., ver. 672.

Nor print any marks upon you] It was a very ancient and a very general custom to carry marks on the body in honour of the object of their worship.  All the castes of the Hindus bear on their foreheads or elsewhere what are called the sectarian marks, which distinguish them, not only in a civil but also in a religious point of view, from each other.  

Most of the barbarous nations lately discovered have their faces, arms, breasts, &c., curiously carved or tattooed, probably for superstitious purposes.  Ancient writers abound with accounts of marks made on the face, arms, &c., in honour of different idols; and to this the inspired penman alludes, Re 13:16,17; 14:9,11; 15:2; 16:2; 19:20; 20:4, where false worshippers are represented as receiving in their hands and in their forehead the marks of the beast.  These were called stigmata stigmata among the Greeks, and to these St. Paul refers when he says, I bear about in my body the MARKS (stigmata) of the Lord Jesus; Ga 6:17.  I have seen several cases where persons have got the figure of the cross, the Virgin Mary, &c., made on their arms, breasts, &c., the skin being first punctured, and then a blue colouring matter rubbed in, which is never afterward effaced.  All these were done for superstitious purposes, and to such things probably the prohibition in this verse refers. Calmet, on this verse, gives several examples. See also Mariner’s Tonga Islands, vol. i. p. 311-313.