Grate onion, cucumber, and celery. Drain well. Combine vegetables, cream cheese, salt, and hot sauce in a medium mixing bowl; beat until smooth.
Remove crust from bread, and cut each slice into four triangles. Coat each piece lightly with mayonnaise. Spread filling on bread slices. Garnish with cucumber slices, if desired.
Alternate method: Position knife blade in food processor bowl; add onion, cucumber, and celery. Process 3 to 5 seconds. Stop processor, and scrape sides of bowl with a rubber spatula. Process an additional 3 to 5 seconds or until vegetables are finely chopped. Remove vegetables, and drain well.