What is a one-sentence summary of the following article?
One simple way to start removing some of the crumbs or debris that may have built up in your knife block is to simply turn the whole thing over. Spend a minute or two shaking it over the trash to help remove crumbs. To help the process along, try using a blow dryer to dislodge crumbs. Attach the crevice tool to the hose, and use it to get down as far as you can into the knife block. That should suction out most of the debris. Stick it in there, using it to get far into the corners. You may need to twist or swirl it around a bit to capture the grime. Clean your tool off from time to time so you are still removing dirt instead of adding it.

Summary:
Turn it over. Try the vacuum. Use a pipe cleaner to get down into the slots.