Shall we ____ across this field instead of going by the road?
A.	come
B.	cut

Note: I’d usually say “walk across.” Is B the answer? If so, what is wrong with A?

cut is the correct answer, walk would also work.
Come implies motion towards the speaker, and clearly the motion is going to away from where the speaker is standing, because it is the speaker who is going to move. So 'go across this field' would also work.