Rake the ground beneath the bird feeder once a week to clean up any seeds the birds scattered on the ground. This also rakes up and removes any newly sprouted seeds before they take hold in the ground.
Vacuum the area under the bird feeder weekly (or more often if you prefer) using a shop vacuum to clear the area of any spilled seeds that may sprout on the ground.
Attach a tray to your bird feeder to catch any seeds that are thrown out of the feeder by the birds. Make sure that the tray is slightly larger than the feeder itself (otherwise it won't catch the seeds) and attach it with screws or glue.
Fill your bird feeder with black oil sunflower seeds, as almost all birds love it and won't leave any behind to sprout. If you fill the feeder with sunflower chips (the hulless version of black oil sunflower seeds), birds will consume it so completely that very little seed will be left behind to sprout.