Spanghew means to throw or jerk something violently into the air. “Especially a frog, etc, as a game,” says my Concise Scots Dictionary. The Oxford English Dictionary concurs. Sadly, I have turned up no details to support this description of what sounds like an especially cruel and primitive sport.
The only sporting connection I can find refers to a horse, not a frog, and it’s the horse that’s doing the throwing: “Hercules had ‘spang-hewed’ so many triers, and the hideous contraction of his resolute back had deterred so many from mounting, that Buckram had began to fear he would have to place him in the only remaining school for incurables, the ’Bus” [that is, he would end his days between the shafts of a London omnibus]. This is from Robert Surtees’ Mr Sponge’s Sporting Tour of 1853.
The origin of second part is obscure — there’s no evidence to link it to any of our usual senses of hew. The first part is the Scots and Northern English dialect spang, originally a verb meaning to spring, leap or bound. The Reverend M C F Morris wrote about it in his Yorkshire Folk Talk in 1892: “It is probably now obsolete, though its disappearance is regrettable, being very expressive in such a phrase as spang thi gaits, i.e. put your best leg foremost. It is, however, still in use in such a phrase as he spang’d him doon, i.e. he threw him violently to the ground”.