Replace the tire.
A bike has a number of systems: propulsion, suspension, braking, steering, etc. Propulsion is one of the least critical. If it fails, you walk home (or call someone for a ride), but otherwise it's not much of a hazard.
Most of the other systems though, a failure while you are on the bike and especially if you are at any significant speed, can lead to significant injury. When any of these systems are compromised, one should ride a bike with great care and prejudice. It might be okay to limp home at a slow speed, making sure to take corners gently, etc. but you should treat the bike skeptically. Don't ask too much of it until it's been repaired.
In the case of a tire (which I'd consider part of the suspension), if it were to fail when you are riding straight on a level surface, that's probably a controllable outcome. But if you're braking heavily, or taking a sharp turn (both activities being things that put added stress on the tire and make it more likely to fail), you could easily lose control of the bike and fall.
There's limited capacity for any of us to judge the degree of damage to that tire. But when I view the photo at its full resolution, it appears to me that it's constructed with a very thin sidewall to start with, and that at least two layers of structural plies have been cut through somehow.
Even a single layer of structure being damaged would in my opinion be cause to replace the tire. You can get away with superficial damage, such as light scraping of the rubber surface, torn tread block, etc. But you do not want the tire to fall apart. The structural elements work together and are critical. If anything is damaged, you can't trust the tire. There's no guarantee that a failure would be gradual. It could be that there's a single thread of ply holding that section of the tire together, and that if it broke, the whole sidewall would fall apart.
Fact is, a new tire is really, really cheap insurance to make sure the bike is safe to ride. The fact that you felt the need to ask the question at all, is sufficient reason to determine that the tire is probably unsafe and needs replacing. Unless you're the type of person to skydive with a 'chute packed by a five-year-old, don't take chances with stuff like that. :)