You can’t pay {W} multiple times to create more than one token each time you resolve Spirit Cairn’s triggered ability.

If a player discards a card during their cleanup step due to having too many cards in hand, any appropriate abilities that trigger on discarding that card (such as Spirit Cairn’s ability) trigger. If this happens, those triggered abilities are put onto the stack and players receive priority in that cleanup step to cast spells or activate abilities (normally, no players may take actions during a cleanup step). Another cleanup step is created following that one.