The incident occurred in Chandor, Gudi, and Paroda villages, according to police.
Of the three crosses, the Alma Khuris cross, located in Chandor village, had been desecrated in the past as well. It was restored only recently.
"We have launched the investigation into the matter, but there is no breakthrough yet. We are considering every possible angle," Quepem police station inspector Pravin Gauns told PTI.
He said the police would identify suspects after getting a decisive lead.
Goa Chief Minister Manohar Parrikar yesterday told reporters that a strict action would be taken against the miscreants.
"Patrolling by police would be intensified in these areas. We won't tolerate such a mischief," he told reporters.