to mark / celebrate an anniversary
When people use "mark an anniversary", is it usually a tragic event, like someone's death, a battle etc? Would you rather use "celebrate" if it's someone's wedding anniversary or something like that?

Question

Answer

To mark = To acknowledge or celebrate (an important event) with a particular action.  It is not tragic.  The event that is being acknowledged or remembered could be happy (a jubilee) or tragic (a war).

To mark would imply an action/event of remembrance or celebration that is of a certain scale.  We would not say, "To mark his birthday, we had a drink in the local pub."  We would say, "To mark the Queen's Diamond Jubilee, a service of thanksgiving was held at Westminster Abbey."