What is this wooden sheet behind my drywall?
It’s undoubtedly a shear wall to resist lateral loads, especially if you live in a “high wind” area or a seismically active area. 

It could also be a reinforced wall for shelving. 

Yes, you can cut through it, or cut openings in it, whether it’s a shear wall or not. I would not make an opening more than 1/4 the height of the wall and not more than square shaped...don’t make it a large rectangle. Also, I’d install framing members at the edge of the opening. (If it’s a load bearing wall, you’ll need to install a header.)