It does not have a root privilege mode. GrapheneOS doesn't weaken any aspect of the standard security model. It has all of the standard security model and features including hardware-based security intact. It greatly improves security rather than doing that.

User accessible root access is available in userdebug (non-production) builds. There's no system for granting root access to apps. It's no different from the stock OS in this regard, but it's a lot more secure than the stock OS.