To desecrate means to treat a sacred place or thing with violent disrespect. The news sometimes reports on vandals who have desecrated tombstones or places of worship.
The word consecrate from the Latin consecrare means "to make sacred." Substituting the prefix con- with de- reverses the meaning. When preparing for a foreign occupation, the military instructs troops not to desecrate sacred sites and risk offending the local population. You can also desecrate someone's memory if you spread malicious lies about him after his death.