I've stuttered significantly during job interviews but I've still been hired. I've been open and honest about my stutter and they've been very accepting of it. There are good people out there who will still give you opportunities to prove yourself despite your disability. I'm earning well into 6 figures and yet I'm a lifelong stutterer. I'm truly blessed even though I stutter. Honesty is the best policy. If they don't hire you because of your stutter, move on and don't look back. It's their loss.