Depends on the situation.
'Get cheap' means become cheap, implying that somebody or something wasn't cheap before.
"Don't get cheap on me. We need to get something better."
'Go cheap' might be used in the same situation, but more often would be used in a situation where somebody doesn't have much money and is forced to be careful.
"We don't have much money for this trip, so we're going to have to go cheap." Note that 'go cheaply' should really be used here, but in spoken English, you would often hear 'go cheap'.