scuff v.

"push along by direct, continuous strength; attempt to move by pushing," Middle English shouven, from Old English scufan, sceofan "push away, thrust, push with violence" (class II strong verb; past tense sceaf, past participle scoven), from Proto-Germanic *skūbanan (source also of Old Norse skufa, Old Frisian skuva, Dutch schuiven, Old High German scioban, German schieben "to push, thrust," Gothic af-skiuban), from PIE root *skeubh- "to shove" (source also of scuffle, shuffle, shovel; likely cognates outside Germanic include Lithuanian skubti "to make haste," skubinti "to hasten").

It has been replaced by push in all but colloquial and nautical usage. The intransitive sense of "press or push forward" was in Old English. Related: Shoved; shoving.

Shove off "leave" (1844) is from the boating sense of "cause to move away from shore by pushing with poles or oars (c. 1600). Shove the queer (1859) was an old expression for "to counterfeit money." Shove it had an earlier sense of "depart" before it became a rude synonym for stick it (by 1941) with implied destination.

"to strike with or as with the open hand," 1520s, of unknown origin, perhaps from Swedish kuffa "to thrust, push." Related: Cuffed; cuffing. As a noun, "a blow with the open hand," from 1560s.