How to delete blog from Twenty Eleven theme?

this is the same for most themes:

set a static front page http://codex.wordpress.org/Creating_a_Static_Front_Page

are you using the ‘showcase’ template for the static front page?

in this case, you need to start by creating a child theme to work with – http://codex.wordpress.org/Child_Themes

then edit showcase.php in the child theme; and remove this section (line 159 to 212):

<section class="recent-posts">
					<h1 class="showcase-heading"><?php _e( 'Recent Posts', 'twentyeleven' ); ?></h1>

					<?php

					// Display our recent posts, showing full content for the very latest, ignoring Aside posts.
					$recent_args = array(
						'order' => 'DESC',
						'post__not_in' => get_option( 'sticky_posts' ),
						'tax_query' => array(
							array(
								'taxonomy' => 'post_format',
								'terms' => array( 'post-format-aside', 'post-format-link', 'post-format-quote', 'post-format-status' ),
								'field' => 'slug',
								'operator' => 'NOT IN',
							),
						),
						'no_found_rows' => true,
					);

					// Our new query for the Recent Posts section.
					$recent = new WP_Query( $recent_args );

					// The first Recent post is displayed normally
					if ( $recent->have_posts() ) : $recent->the_post();

						// Set $more to 0 in order to only get the first part of the post.
						global $more;
						$more = 0;

						get_template_part( 'content', get_post_format() );

						echo '<ol class="other-recent-posts">';

					endif;

					// For all other recent posts, just display the title and comment status.
					while ( $recent->have_posts() ) : $recent->the_post(); ?>

						<li class="entry-title">
							<a href="<?php the_permalink(); ?>" title="<?php printf( esc_attr__( 'Permalink to %s', 'twentyeleven' ), the_title_attribute( 'echo=0' ) ); ?>" rel="bookmark"><?php the_title(); ?></a>
							<span class="comments-link">
								<?php comments_popup_link( '<span class="leave-reply">' . __( 'Leave a reply', 'twentyeleven' ) . '</span>', __( '<b>1</b> Reply', 'twentyeleven' ), __( '<b>%</b> Replies', 'twentyeleven' ) ); ?>
							</span>
						</li>

					<?php
					endwhile;

					// If we had some posts, close the <ol>
					if ( $recent->post_count > 0 )
						echo '</ol>';
					?>
				</section><!-- .recent-posts -->

if this is not it, please post a link to your site to illustrate your situation.