The effect of "Jurrac Gallim" will activate even if "Jurrac Gallim" and the other battling monster are both destroyed by battle; however, the other monster is not on the field, so the effect of "Jurrac Gallim" is not applied. Thus, the opponent cannot discard from his hand to negate the effect of "Jurrac Gallim".[3]
If a player discards one card to negate the effect of "Jurrac Gallim", then it is treated as the player discarding by the effect of an opponent's card.[2]
Example: If you discard "Goldd, Wu-Lord of Dark World" to negate the effect of the opponent's "Jurrac Gallim", then "Goldd, Wu-Lord of Dark World" is treated as being "discarded by the effect of an opponent's card", so you can select and destroy two cards on the opponent's side of the field.[2]