1" concrete backer behind 1964 tile in bath

[Christopher Bayes]

We are about to renovate a 1964 house in Florida. 

When we began chipping off the old 4x4 tile on the bathroom walls we found a slab behind each wall about an inch thick of concrete to which the tiles are adhered to directly.

Is there an easy way to remove the tiles or should be just demo the entire slab, tile and all and just replace with 1/4" concrete board on the remodel?

Thanks