Exclude category by slug for for each loop

As I already stated, straight from the codex

exclude

(string) Excludes one or more categories from the list generated by wp_list_categories. This parameter takes a comma-separated list of categories by unique ID, in ascending order

As you have stated, you have to use the category slug. To make this possible and dynamic, I think the best will be to write your own wrapper function to achieve this. We are going to use get_terms() (which is used by get_categories() internally) to get our categories and get_term_by() to get the category ID so that we can pass that to get_terms()

Here is the function, I have commented it well for better understanding (Requires PHP 5.4+)

function exclude_term_by( $taxonomy = 'category', $args = [], $exclude = [] )
{
    /*
     * If there are no term slugs to exclude or if $exclude is not a valid array, return get_terms
     */
    if ( empty( $exclude ) || !is_array( $exclude ) )
        return get_terms( $taxonomy, $args );

    /*
     * If we reach this point, then we have terms to exclude by slug
     * Simply continue the process. 
     */ 
    foreach ( $exclude as $value ) {

            /*
             * Use get_term_by to get the term ID and add ID's to an array
             */
            $term_objects = get_term_by( 'slug', $value, $taxonomy );
            $term_ids[] = (int) $term_objects->term_id;

    }

    /*
     * Set up the exclude parameter with an array of ids from $term_ids
     */
    $excluded_ids = [
        'exclude' => $term_ids
    ];

    /*
     * Merge the user passed arguments $args with the excluded terms $excluded_ids
     * If any value is passed to $args['exclude'], it will be ignored
     */
    $merged_arguments = array_merge( $args, $excluded_ids );

    /*
     * Lets pass everything to get_terms
     */
    $terms = get_terms( $taxonomy, $merged_arguments ); 

    /*
     * Return the results from get_terms
     */
    return $terms;
}

Before I go into usage, here are a few notes

• The first parameter, $taxonomy is the particular taxonomy to pass to get_terms() inside the function, it defaults to category

• The second parameter, $args takes the same parameters as get_terms(). Just a note, if the third parameter is set, the default exclude parameter’s value is ignored if anything is passed to it. This value will be overridden by whatever is passed to $exclude. If nothing is passed to this parameter, and anything is passed to $exclude, you need to pass an empty array as value

• The third parameter, $excludes takes an array of term slugs which should be excluded. If the value is not a valid array, get_terms() will be returned without excluding the necessary terms, so be sure to pass an array of slugs

• Treat the output from the function in the same way you would with get_terms(). Remember, you should also check for empty values and WP_Error objects before using the value from the function

• Modify and abuse the code as you see fit

Now for the usage in your template files. Note the empty array passed to the $args parameter if anything is passed to the $exclude parameter

$terms = exclude_term_by( 'category', [], ['term-slug-one', 'term-slug-two'] );
if ( !empty( $terms ) && !is_wp_error( $terms ) ) {
    ?><pre><?php var_dump($terms); ?></pre><?php
}   

For any extra info on usage, see get_terms().