我這樣翻譯可以嗎？

Your translation is wrong because of the wrong use of present participle.

The sentence below is an example on the use of "there being".
There being no bananas left (at home), I went to the supermarket to buy some.
(家中沒有香蕉，我到超市去買。)

Below is the translation of the sentence 我到達超市時，沒有香蕉賣了 :
When I got to the supermarket, there were no more bananas left.

When I got to the supermarket, bananas are all sold out (賣完).

我到達超市時，沒有香蕉賣了。
When I arrived the supermarket & found the bananas
were all sold out.

no3lunch's response is good and he gets the points~~

Error and Correction:-
There (was) no bananas left (for me to buy) in the supermarket.
When (grammar) 'there'' is in front position of sentence;
(1)bananas,(2)for me to buy (3)supermarket,
Therefore why use got? (=past tense go=went ?);
therefore why use being in past tense unless adv.cl.?
(i.e,There being no bananas left, I was (disappointed/dissatisfied/frustrated/ adj should be used to fill in the missing word) in the supermarket.

點解你用got﹖
呢句你用past tense，點解用being﹖

you should write:
When i had arrived supermarket,there had no bananas left.