Pyrethrin* is an organic compound harvested from the Fall ornamental plant, Chrysanthemum (Fall Mums)! This compound is often considered compliant for organic gardening as it breaks down quickly and is not absorbed by the plant. Though, be careful with outside use, if you accidentally spray a bee it will have the same result as spraying a Spidermite! As Pyrethrin breaks down so fast, this shouldn't be much of a concern unless you are actively seeking out and spraying garden bugs around your yard.
Pyrethrin is found naturally in Fall Mums, so as an experiment you can actually take dried Mum flowers, grind them to a powder and test this powder on a colony of controlled Spidermites! Though it won't be as effective as the mixed components of Safer's End All, it still makes for an exciting experiment!