is there a way to remove featured image from blog page and single page

If you don’t want to modify the template files directly, you could always make use of the post_thumbnail_html filter:

function wpse70960_filter_post_thumbnail_html( $html ) {
    if ( ( is_home() || is_single() ) {
        return '';
    } else {
        return $html;
    }
}
add_filter( 'post_thumbnail_html', 'wpse70960_filter_get_post_thumbnail_html' );

This code snippet goes either in your functions.php file or in a custom (mu-) plugin.

Edit

From your comment:

Im using a static page for the homepage and blog is using a new page I created in the WP CMS using a template file called Blog page. The homepage is rending the featured image for posts which is what I need. I want to avoid using the Featured image in the blog page and the singe page.

There are two approaches:

1. Don’t use a custom page template to display the blog posts index. It’s not necessary. Assuming that template file is template-blog.php, copy that file, and rename it as home.php. Then go to Dashboard -> Settings -> Reading, and set “Page for posts” to the Page that is/was using the custom page template. That should solve the problem, and ensure that you don’t lose any formatting.

2. Alternately, inside your filter callback, add the following:

   global $post;
   $page_template = get_post_meta( $post->ID, '_wp_page_template', true );
   if ( ( is_home() is_single() || 'template-blog.php' == $page_template ) {
       // etc.
   }
   

Edit 2

Full code, using alternative #2 above:

function wpse70960_filter_post_thumbnail_html( $html ) {
    global $post;
    $page_template = get_post_meta( $post->ID, '_wp_page_template', true );
    if ( ( is_home() || is_single() || 'template-blog.php' == $page_template ) {
        return '';
    } else {
        return $html;
    }
}
add_filter( 'post_thumbnail_html', 'wpse70960_filter_get_post_thumbnail_html' );