Wikipedia is of no help. Google returns a question and answer that says it’s a direct translation from Hawai’ian, but no reference.
Is this some pidgin thing where the past tense is not used? Apparently it originated in Japan, which easily explains why it’s popular in Hawai’i.
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Typo fixed in thread title.
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“Shave Ice” has always sounded wrong to me, but I have no idea why most vendors seem to use that term.
Hawaii used to belong to the British, who took the d to make iced water.
When I have actually pondered this, I thought they were using the term “Hawaiian Shave” to describe the type of shave the ice gets.
It certainly wouldn’t be the first time that the past tense ending was dropped, whether out of ignorance, laziness, or what have you. I’ve seen plenty of signs/ads touting “old fashion” businesses.
I assume for the same reason that people talk about “ice tea” and “daylight savings time” - laziness and habit.
I’m from Hawaii and it’s because of the way local’s talk. Hawaiian Pidgin has a bunch of clipped and abbreviated phrases and words.
I hope dat wen answer yo’ question, cuz.
Not everybody says shave ice.
Excuse me? Hawaii never belonged to the British. I used to live there, and while the godless Brits did discover it first, and there was some British influence, it never ever belonged to Britain.
From the website:
Hawaiian Shaved Ice.com
321 Goldsboro Street
Newton Grove, NC 28366
Doesn’t look very Hawaiian to me - they probably do kalua pork with barbecue sauce down there. It does explain the superfluous “d” though. 
Seriously, re: the OP, my wife grew up in Hawaii, and after 16 years with her, hearing “shaved ice” sounds wrong to me now.
Yeah, but that site is from North Carolina. Probably someone who went to Matsumoto Shave Ice on vacation and decided to spread it to the haolies.
The Matsumoto store is the most iconic and they use the spelling.
Also, theWaiola Shave Ice is clearly superior IMHO. The Google place name says “Shaved Ice” but that’s user-generated, the actual store sign calls it “Shave Ice”
Honestly, if anyone from Hawaii said Shaved Ice I’d assume they’re translating for non-locals.
EDIT: Ninjaed!
No, bra, dat neva answer da question. 
Seriously, there isn’t anything in there about clipped “ed” for adjectives. I’m sure it has something to do with pidgin, but are there other similar examples? Like: “can peaches” or “smoke meat”.
Just wondering if there is a pattern, or if this is an isolated instance.
While we’re on the subject, what’s with the Hawai’ian colloquial pronunciation of “bro”? Sounds like they’re saying “bra.”
I wasn’t aware this was why do Hawaiians say use the term shave ice question. I thought there was confusion that everybody uses that term. We don’t.
Cf. “skim milk”. It’s SKIMMED milk, damn it!
It’s short for “braddah”, which is pidgin for “brother.”
Huh?
I think this is one where the Hawaiians have a clear advantage. When pronounced the first syllable of *brother *is way closer to *bra *than bro.
I don’t think it’s specifically for adjectives, I think it’s a general shortening and clipping of words. Da kine is from* The Kind*, its just been shortened and massaged a bit. Li’dat.
“Shave” ice is one of my pet peeves. Thank you for posting about it.