"Ut quid" there is usually translated as "why", but I know the usual word for "why" is "cur". So, why the weird phrasing? I can kind of see how "ut quid" can mean "why", as it literally translates at "so-that what", but it seems to me the phrasing is weird.
Jerome is translating the Greek here:
ἱνατί με ἐγκατέλιπες (Mt. 27.46)
The phrase ut quid then is a translation specifically of ἱνατί (especially when spelled out separately as ἵνα τί). Both ἵνα and ut for example are used to create a purpose clause, and τί is simply the Greek neuter singular interrogative, corresponding with quid.
This is common enough in Greek literature, as the LSJ shows:
c. [ἵνα] τί (sc. γένηται); to what end? either abs. or as a question, Ar.Ec.719; or with a Verb following, Id.Pax 409, cf. Pl.Ap.26d, etc.; ἵ. δὴ τί; Ar.Nu.1192.
I don't see this particular usage mentioned in Lewis and Short under ut, though, and I don't see it used in this way quickly scanning PHI results, so I tentatively chalk it up as Jerome being literal with the Greek.
Interestingly, in the Psalms it is translated more normally:
quare me dereliquisti?
This is likely because Jerome is translating here from the Hebrew לָמָ֣ה, which is a more straightforward way of asking "why."
(In Latin, cur might be one word for "why", but quare is another common one; see e.g. Catullus 85: quare id faciam fortasse requiris, "why do I do this, perhaps you are asking.")
In the Iuxta Hebraicum (Weber and Gryson), ut quid shows up 1x, quare 23x.
In the Iuxta Septuaginta (Gallicanum), ut quid shows up 7x, quare 15x.
Cur shows up in the Iuxta Septuaginta 1x (XLVIII.6 cur timebo in die malo iniquitas calcanei mei circumdabit me). Iuxta Hebraicum uses quare in XLVIII.6 and the Psalterium Romanum uses ut quid. The Psalterium Romanum does not seem to use cur.