Peel cucumber, remove seeds and grate into a bowl. Add salt and let sit until cucumber is slightly soft and water has collected, approx. 30 min. Squeeze and drain cucumber. Add minced garlic, yogurt, olive oil, vinegar, pepper and mint. Mix well, taste and adjust seasonings. Refrigerate until ready to use.
Drain canned tomatoes, reserve juice and dice tomatoes; set aside. In a lg, heavy skillet over med-high heat: add olive oil, then onions and sauté until browned, 4 min. Add garlic and sauté until fragrant, approx. 1 min. Add diced tomatoes, salt, pepper, sugar and vinegar. Cook until juice almost evaporates. Add cherry tomatoes and oregano and stir. Taste and adjust seasonings. Keep warm. If you desire a thinner sauce, add some reserved tomato juice after the sauce has been reduced.
On a grill, over high heat, cook sausages approx. 8 min, turning three times. Remove and rest 2 min. Slice sausages. Meanwhile, lightly brush flat breads with oil on both sides. Grill bread until warmed and grill marks appear, flipping once, approx. 30 sec total time. To assemble, place grilled bread onto each plate and spread with approx. 1/4 c Tomato Sauce. Arrange 5-6 sausage slices on top, then drizzle with more tomato sauce. Top with Tzatziki, crumbled feta and approx. 6 mint leaves.
* Substitute packaged tzatziki from our grocery deli section, located alongside the dips and spreads.