Take a look at the get_adjacent_post
function.
It takes three paramters, all of which are optional:
- a boolean, whether the post should be from the same category
- a string of category IDs that should be excluded
- a boolean, whether the previous (true) or next (false) post should be retrieved.
Hence the previous post, regardless of category can be retrieved via
$prev_post = get_adjacent_post( false, '', true );
and the next via
$next_post = get_adjacent_post( false, '', false );
If successful, the function will return a complete post object, hence:
echo $prev_post->post_excerpt;
should do.