Camera shake when shooting with 70-200 f/2.8 on a tripod.

[neuroanatomist]

The vibration caused by the mirror closing cannot affect the image - at that point, no light is hitting the sensor.

OTOH, the mirror opening can affect the image - are you using mirror lock up (MLU) with a 2-sec timer?

Using Live View with silent mode 1 (default) can also help - that mode uses an electronic first curtain which further reduces vibration. Between that and MLU with the timer delay, the only camera-induced vibration should be coming from the second shutter curtain - you really shouldn't even notice that affecting the image.