Translation:I eat with a round spoon.
私はバナナですよ。 (Apologies if you weren't going for the Don Hertzfeld's "Rejected" reference)
で can be used to mean "by means of"
スプーンでたべます "I eat by means of a spoon"
自転車で学校に行きます "I go to school by means of a bicycle"
Is there something wrong with "I eat using a round spoon," or does Duo need to be educated again?
I think it's both. Sometimes the same word can be written with different kanji.