To remove the plastic liners so that the bag can be recycled, the bag must first be turned inside out. Once reversed, grab hold of the inner plastic liner and pull it away from the paper. After this inner liner has been removed, peel back the layers of paper until you've located the second plastic liner. Once you have done that the paper can be placed in the recycling bin with the mixed paper. 

You can also reuse these bags for other purposes. By finding other uses for those pet food bags, you'll saving money while deferring waste headed to the landfill.

• Use as garbage bags. Some dogs and cats go through a few a month, so when you empty a bag, it becomes the kitchen garbage. It may not be recyclable, but it's going to end up as landfill anyway.
• Use as shelf liners in the garage to prevent rust or other stains, especially on metal shelving
• For shipping items, cat food bags make great waterproof mailers. Turn the bag inside out, pack the item inside the bag, then tape it shut. The mailing address can be written on the outside with a permanent marker or an address label
• Store greasy automotive or tractor parts, A large dog food bag is ideal for this use 
• Great for holding ashes, sawdust or other dusty material that is  headed for the trash, since those items have to be in a securely sealed container when put out for trash collection
• Use to protect surfaces, slice a large dog or cat food bag open along the side and bottom seam, so you can create a water proof pad that measures approximately three by three feet. This will protect the garage floor when changing the oil in a chain saw, lawn mower or car. Or use to protect a table surface when painting craft items or repotting plants
• Maybe someone in your locality could use your empty pet food bags