Rusty front frame rails

I am working on a 1968 mustang coupe that I mostly restored ten years ago and now has rust rot in two small sections of the bottom of the front framerails where the rear of the rail meets the floor supports near the torque boxes. I have checked the rest of the rails and they are solid. I jacked up the car about 16 inches in four places. I have two jack stands @ the beginning of the rear frame rails and two on the floor supports. I have removed the gas tank and fuel line. My question: Is it Safe/Smart to cut out these rusty sections and weld in patches with and engine and transmission still in the car or do they have to be removed? If not, how should I properly support the car so not to warp anything? the engine is only a 200ci six.

You could get by without removing the engine if you add more support, however, if it were mine, I would not try it. I would take the engine and trans out (speaking from experience it would be a whole lot easier to work on and you reduce the risk getting it out of shape). You will probably have to move the jackstand, that is shown in the picture, farther to the rear to work in that area and you will need to add jackstands under the forward end of the frame rails (support both sides) at a minimum (chances are that the front end has drooped a little just from being supported like it is now). An export brace really stiffens the front end, put one in before cutting anything.

If the frame rails are shot the torque boxes should be looked at. Ususally it's a pkg deal. You will be better off replacing the frame rails and torque boxes. Most likely you will be spending about the same amount of time and money just replacing them rather than repairing them. Then after putting in all the time of repairng them you will wish you did replace them.

I would agree with valleyfirearms, generally rust is a lot worse than what you see. Once you start cutting away the rusted area that you can see, the extent of the deterioration becomes apparent and has grown from the original estimate.