Wordpress - Custom post types filtered by taxonomy using REST API v2

Ok, the solution was:

example.com/wp-json/wp/v2/works?work_type=10

It views the work_types as id's. You can view the id's in:

example.com/wp-json/wp/v2/works

I installed the WP REST Filter plugin and then i'm able to filter post by category slug like:

http://www.example.com/wp-json/wp/v2/my_custom_posts?filter[my_custom_taxomony]=my_custom_taxonomy_slug

in your case:

http://www.example.com/wp-json/wp/v2/works?filter[work_type]=building

If you really need to use slug as url parameter you can add a custom filter, take a look to rest_{$this->post_type}_query hook

You can do something like that (post_type: work, taxonomy: work_type):

/**
 * Filter work post type by work_type slug
 *
 * @param array $args
 * @param WP_Rest_Rquest $request
 * @return array $args
 */
function filter_rest_work_query( $args, $request ) { 
    $params = $request->get_params(); 
    if(isset($params['work_type_slug'])){
        $args['tax_query'] = array(
            array(
                'taxonomy' => 'work_type',
                'field' => 'slug',
                'terms' => explode(',', $params['work_type_slug'])
            )
        );
    }
    return $args; 
}   
// add the filter 
add_filter( "rest_work_query", 'filter_rest_work_query', 10, 2 ); 

and then

https://example.com/wp-json/wp/v2/work?work_type_slug=slug01,slug02