In biomedical applications, galvanic electrode voltage and noise will degrade signal! and induce galvanic offsets, so for example, this is why "active guarding" is used to derive the common mode voltage then buffered and fed back to "right leg" (arbitrary). (hint look up)
Otherwise in general applications a select on test, DC null adjust is required, but if not possible a HPF such as @Andy's integrated DC error negative feedback to input offset control. This can be designed for any low frequency cutoff of HPF.
Here's an example of a precision INA with extra op amp for offset adjustments with an example of 10V common mode and 10mV dc offset with gain x1000 
ref http://support.technologicalarts.ca/docs/Components/amp04.pdf