How can i remove the posts category class names from body_class

This could be solved via CSS as well. Just set up declarations for the special cases where there is overlap between categories:

.category-cars { background-color: #f00; }
.category-bikes,
.category-cars.category-bikes { background-color: #0f0; }

This will give any posts that are in both bikes and cars the same background color as those used in the bikes category.