Were there any type of animals that were destroyed completely by the Mabul? (For example - Is there any source that there were dinosaurs or any other type of wildlife and they were destroyed by the Mabul?)
To answer the question in the title, according to Bereshit Rabbah 31:13 the Re'em (and some say it's offspring) were not brought into the Ark. R' Nechemia says they were strapped to the side of the ark.
Per the Malbim (HaTorah VeHamitzva 7:23) there was some wildlife that was destroyed completely in the Mabul.
והנה שהרבה נשארו עצמותיהם החזקים כמטילי ברזל ולא נמוחו, בכל זאת נמוחו מן הארץ כי ע''י שטף המים הובלו הפגרים לתוך העמקים ורובם נבלעו בעמקי תהום, אשר האדמה פצתה את פיה מעומק תהום רבה וירדו כמה אלפים אמה לעמקי שאול, עד שבצאת נח מן התיבה לא מצא שום רושם מפגרי בעלי חיים ועצמות הענקים ובעלי חיים הגדולים שהיו קודם המבול
First and foremost, according to the accepted scientific consensus, dinosaurs died tens of millions of years before humans ever walked the Earth. (Just wanted to get that out of the way before we continue.)
Based on a simple reading of the text (p'shat), two individuals of all land-based and air-based species of animals entered the Teiva\Ark. It follows that there are no species of animals that were completely destroyed by the Mabul\Flood.
(Fish species were not taken into the ark, but they aren't mentioned as being destroyed, either. It is unclear how plants survived, since בראשית Genesis 7:23 mentions that they were destroyed, and Noach did not take any plants other than food into the ark.)
According to the Midrash (מדרש רבה בראשית פרשה ט אות י), God created many worlds, and destroyed them, before our world was created. The dinosaurs may have been part of one the earlier worlds, and were destroyed before ours was created. For more information, please see:
בראשית Genesis (1917 JPS Translation):
Chapter 6: 19 And of every living thing of all flesh (וּמִכָּל-הָחַי מִכָּל-בָּשָׂר), two of every sort shalt thou bring into the ark, to keep them alive with thee; they shall be male and female. 20 Of the fowl after their kind, and of the cattle after their kind, of every creeping thing of the ground (מִכֹּל רֶמֶשׂ הָאֲדָמָה) after its kind, two of every sort shall come unto thee, to keep them alive.
Chapter 7: 8 Of clean beasts, and of beasts that are not clean, and of fowls, and of every thing that creepeth upon the groun(וְכֹל אֲשֶׁר-רֹמֵשׂ עַל-הָאֲדָמָה)d, 9 there went in two and two unto Noah into the ark, male and female, as God commanded Noah.
13 In the selfsame day entered Noah, and Shem, and Ham, and Japheth, the sons of Noah, and Noah's wife, and the three wives of his sons with them, into the ark; 14 they, and every beast after its kind, and all the cattle after their kind, and every creeping thing that creepeth upon the earth after its kind, and every fowl after its kind, every bird of every sort. 15 And they went in unto Noah into the ark, two and two of all flesh wherein is the breath of life. (שְׁנַיִם שְׁנַיִם מִכָּל-הַבָּשָׂר, אֲשֶׁר-בּוֹ רוּחַ חַיִּים.)
Chapter 8: 18 And Noah went forth, and his sons, and his wife, and his sons' wives with him; 19 every beast, every creeping thing, and every fowl, whatsoever moveth upon the earth, after their families; went forth out of the ark.