How do you deseed Concord grapes?

I agree with HalfPint. Don't puree as you'll also puree the seeds and that makes them much more difficult to remove. If you don't have a food mill, push your crushed/mashed fruit through a sieve. Depending on your final use (for example, if you want a clear juice either to drink or as a base for jelly) you may want to take the seived fruit one step further and strain through a jelly bag to remove sediment as well as seeds.

You can crush them and put throw a food mill.

There's no easy way to de-seed them if you are using them whole. However, if you are pureeing them first to make a jam or a spread for a pie, you can strain them through a fine sieve and that will remove the seeds