The focusing system used by the camera when you are using the viewfinder is an independent system from the focusing system used when you are using Live View.
Each system is designed and operates completely separately from the other. One works when the mirror is flipped down and the imaging sensor is "blind". The other works when the mirror is flipped up and the dedicated PDAF (Phase Detection Auto Focus) sensor is "blind" along with the viewfinder.
You haven't given us much to go on with regard to what might be causing the PDAF system to not work when using the viewfinder to shoot. You might check the following:
- Make sure you're actually telling the camera to initiate autofocus. It's possible via the settings menu to decouple AF start from a shutter button half-press. There's an option to only initiate metering with a shutter button half-press and assign AF start to another button, typically one on the back of the camera that can be reached by your right thumb without moving your shutter finger off the shutter button.
- Inspect the primary and secondary mirror to be sure light from the lens is being properly sent to the PDAF array in the floor of the mirrorbox.


Should you attempt to fix any obvious problems with the primary or secondary mirrors yourself?
As much as I hate to use the old cliche, this is pretty much a case of, "If you have to ask how, you probably shouldn't be doing it." Mirror adjustments are delicate and must be done precisely. It doesn't take much misalignment at all of the mirror (and the attached secondary mirror) to render a camera's AF system completely useless. The optical path from the lens to the AF sensor via the secondary mirror must be exactly the same length as the optical path from the lens to the camera's sensor. The same is true of manual focus: The optical distance from lens via the mirror to the view/focusing screen at the top of the light box just below the prism must match the optical distance from the lens to sensor.