Does the word beast have a short vowel sound?

No. When two vowels are next to each other, the general phonics rule is to pronounce the long sound of the first vowel while the second is silent.

Beast = Bēst or "Beest"

Road = Rōd or "Rode"

Weird = Wērd or "Weerd"

There are, of course, exceptions, but this is the general rule.