To be clear: This is NOT a safe or recommended method for bypassing the differential for any prolonged driving. Doing so will render your 4WD system inoperable, and could lead to serious damage if you attempt to drive the vehicle. The front wheels will be free-spinning, and the differential will be under unnecessary stress if the vehicle is moving.
If you need to bypass the differential for a specific repair or diagnostic reason, there are safer and more appropriate methods, such as disconnecting the driveshaft or using specific tools to disconnect components within the differential. Simply removing the axle shafts is a dangerous shortcut.
Before attempting any work on your vehicle, consult a repair manual specific to your 1999 Chevy Tahoe. This will provide step-by-step instructions and safety precautions. If you are not comfortable performing this type of work yourself, take your vehicle to a qualified mechanic.