Exegesis:
tō tuptonti se epi tēn siagona pareche kai tēn allēn ‘to him who strikes you on the cheek, present the other also.’ Note that vv. 29f are in the singular as contrasted with what precedes and what follows. tō tuptonti is dative of advantage with pareche.
tuptō ‘to strike,’ ‘to beat,’ in Luke always literally.
siagōn (only here and Mt. 5.39 in the N.T.) ‘jawbone,’ hence ‘cheek.’
parechō ‘to give,’ ‘to present,’ ‘to grant,’ ‘to bring about.’
kai apo tou airontos sou to himation ‘and from him who takes your upper-garment.’ The phrase goes with the main verb mē kōlusēs ‘do not keep back.’ kai introduces the clause as parallel to the preceding one. sou is possessive genitive with to himation. The latter refers here to the “upper and more valuable garment”.
kai ton chitōna mē kolusēs ‘do not keep back your undergarment as well.’ For chitōn cf. on 3.11. kai ‘likewise,’ ‘as well.’
kōluō ‘to hinder,’ ‘to prevent,’ ‘to refuse.’ Here with apo ‘to keep back from.’
Translation:
The construction to him who strikes…, offer … may better be rendered, ‘when someone strikes…, offer him’; similarly the constructions in vv. 29b, 30.
Who strikes you on the cheek, or, ‘on one cheek’ (Translator’s New Testament, Balinese), ‘on the cheek at one side’ (some Indonesian languages); or, where the use of a specific verb is more idiomatic, ‘who slaps-on-the-face/cheek you at one side.’ Cheek. In Sranan Tongo the term literally means ‘side-of-face,’ corresponding with ‘the other side’ in the next clause.
Offer the other, or, ‘offer (him) the other cheek, or, (the cheek at) the other side.’ Other possible renderings of the verb are, ‘turn (to him)’ (An American Translation, Nieuwe Vertaling, Sranan Tongo, Trukese), ‘make (to be) in front of him’ (Marathi), “let him hit” (Good News Translation).
Also means ‘in addition (to it),’ ‘to be treated similarly.’
Cloak and coat, referring to an outer and an inner garment. To render cloak some versions have chosen a term referring to a non-indigenous piece of dress because it resembled the type of garment referred to in the original. This is advisable only, if the dress in question has been commonly accepted in the receptor culture. The coat, or, ‘shirt’ (for which cf. also on 3.11) is mentioned here as example of the necessities of life; therefore one should avoid the use of a term referring to a garment that is considered a luxury in the receptor culture.
Do not withhold, or, ‘do not refuse,’ ‘do not oppose his taking’ (Marathi); or, positively stated, “let him have” (New English Bible, Good News Translation) ‘allow him to take’ (Tae’).
As well, or, ‘in addition to it.’
Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.