This is a perfect idea for reuse, recycle. This kind of thing makes me wish I had a sewing machine and knew how to use it! I have a HUGE bag of old t-shirts in the garage.
How To: Trim Your Fashion Footprint By Making This DIY Shopping Bag | Creativity on GOOD.
Marlene Dotterer 
Very cute, but keep in mind they stretch a lot, and should not be used for heavy loads.
Yeah, I bet they do stretch. I think I’d rather just skip cutting out the strips, and use the full bag for carrying things. I think it would stretch less, although it would never be useful for very heavy items.