The completed crossword

An explanation of the clues
Across:
1A. Finished sculpture is a total letdown (8,4)
COMPLETE BUST (Refers to both a finished sculpture, and a total letdown) -- credit to GentlePurpleRain
8A. 8. Exist as god of secret material (3)
BRA ? B+RA. "Exist" is B; RA is the Egyptian god of the sun
9A. Rhetorical Spanish street has eleven variations (7)
LEXICAL: anagram of CALLE+XI
10A. Measure boundless squats/tumbles at open-source hub (5)
QUOTA: boundless squats = QUAT, open-source = O, O is the hub, so QUOAT, tumbles at the hub QUOTA - credit to LeppyR64
13A. Very first to engrave on kind of flowering plant (5)
VETCH: V+ETCH (first letter of "very" plus etch = engrave)
14A. Break commoner's first-half astounding lead (5)
COMMA: first half of commoner is COMM, first letter of astounding is A
15A. Baby chicken's two eyes (7)
PEEPERS(!): double definition
17A. Single cell busts a ring beam (6)
AMOEBA anagram of A+O("ring")+BEAM
19A. Highest point of a weird, airy shrubbery (7)
TOPIARY: TOP(highest point) + anagram of AIRY
20A. Flag penne pasta, in one end and out the other, first; timeless agent, second (7)
PENNANT: first, take either end of PENNe pastA; second, "agent" minus age (time) = NT
22A. Atrocious gruel is knocked down a peg, gets eighth new start (6)
HORRID (Atrocious = horrid; gruel = porridge, knocked down a peg (remove the word peg) = orrid; gets eighth new start = use the eighth letter of the alphabet (H) to give it a "new start" (put it on the beginning)) -- credit to GentlePurpleRain
27a. Confuse right tonsil with another bodily cavity (7)
NOSTRIL: anagram of R TONSIL :D !!
27b. No initial shortage of endlessly tall half-giants in regret (9)
NOSTALGIA: NO + S (initial letter of shortage) + TAL (tall without final letter) + GIA (half of "giants"). As @GentlePurpleRain anticipated, this entry spirals around the blue square.
29A. A site to the west-southwest? Turn around, you're mixing it up with a vulnerable species (5)
VENUE: anagram of ENE+VU (West-southwest turned around is east-northeast, or ENE. (Thanks @GentlePurpleRain.) Vulnerable species is conservation status VU.
30A. In a surprise twist, three hundred Greeks take in Eastern European catholic (5)
UNIAT: anagram ("surprise twist") of TAU+IN. tau has a value of 300 in Greek numerals and Uniate relates to certain eastern European Christian communities -- credit to Pete
31A. From right to left, feed like cattle on sugary coating (5)
GLAZE (Sugary coating = glaze. Feed like cattle = graze, and change the right to a left (R to L) to give glaze) -- credit to GentlePurpleRain
32A. Cheese has its own chocolatey dessert (7)
BROWNIE: BRIE containing OWN
33A. Residual powder has become obscured (3)
ASH: anagram of "has"
34A. Toothy birds, left unchained, become cutthroat (12)
BLOODTHIRSTY(!): anagram of TOOTHY BIRDS L
Down:
1D. California company's cotton cloth (6)
CALICO (California Company, and calico is a type of cotton cloth) -- credit to GentlePurpleRain
2D. Top ten mixed martial artists start mauling you and I horribly (7)
MAXIMUM: anagram of X+MMA+M+UI (ten = X, mixed martial arts = MMA, start of "mauling" = M, you and I = UI)
3D. Running late, single cats make milk (7)
LACTATE (Not entirely sure, but single cats = cat, mix with late to get anagram of lactate (make milk). -- credit to GentlePurpleRain
4D. At center, all eyes on friend flipping a fish (7)
TILAPIA: All eyes on friend = I + PAL + I, At center = A + IPALI + T, Flipping = TILAPIA – credit to LeppyR64
5D. Legacy spoke of insect's adventure (7)
BEQUEST: homophone (Bee Quest!)
6D. Hold roast over cooking range (5)
STOVE: hidden in roaST OVEr
7D. Cathy capsizes a boat (5)
YACHT (Cathy anagrams to yacht, which is a boat) -- credit to GentlePurpleRain
8D. Flyer's flutters (4)
BATS: double def.
11D. Emphasize that you stuffed yourself full of stomach pastes (9)
OVERSTATE: "you stuffed yourself" is OVERATE; it's full of ST which is the "stomach" (interior) of "pastes". –- credit to LeppyR64
12D. Dog misbehaves once in a rolling tire (7)
TERRIER: TIER(anagram of "tire") containing ERR
16D. Dry-injected polysaccharides (4)
ARID: contained in polysaccharides
17D. Truly, name is awful (4)
AMEN: anagram of "name"
18D. Self-ambition makes an unfortunate point (3,4)
OWN GOAL: double definition (going out on a limb here as I know nothing about sports, but I believe a score on one's own goal is unfortunate)
21D. Destroy with blend of root and condensed performance-enhancing drugs (7)
TORPEDO ("condensed performance-enhancing drugs" gives PED; torpedo is an anagram of "root ped" and things can be destroyed with it) -- credit to rand al'thor
22D. Fish in simple shelter has an incomplete alibi (7)
HALIBUT : HUT containing ALIB ("alibi" missing final letter)
23D. Voila! I reveal original mashed pasta (7)
RAVIOLI: anagram of VOILA+I+R (first letter of "reveal")
24D. Turns evildoing from head to toe (7)
INNINGS: take the first letter of SINNING and move it to the end
25D. Say hear-say, mostly? Blasphemy! (6)
HERESY: here+sy (homophone of "hear" = HERE, most of "say" = SY)
26D. Painting of country with masthead (5)
MURAL: M+URAL (first letter of "mast" replacing the first letter of rural)
27D. It's nearly night! (4)
NIGH: most of "night"
28D. If you're this tall, you have to stop (5)
STALL: concealed in "thiS TALL"