The Stuttering Foundation states "The research is conclusive that people who stutter perform successfully in a range of jobs that require communication skills, from sales to medicine to public relations. However, this may not be evident during the initial interview, perhaps the most stressful speaking situation for everyone, much less someone who stutters. The best way to approach an employee’s stuttering is through honest communication and by refraining from making assumptions about job-related abilities and skills."
A brochure about stuttering is available to take with you on a job interview. Download it at http://www.stutteringhelp.org/DeskLeftDefault.aspx?TabID=13 and give it to the interviewer while telling them you stutter.
The most important thing for stutterers to remember is that it is best to tell the interviewer that you stutter. By doing this at the beginning of the interview and letting them know that stuttering will not hinder work performance, the interview will be much easier. You will stutter more if you try to hide the fact that you stutter. You will also be concentrating more on that then on the best answers to the questions because you will be trying to avoid using words that give you problems.
Get a friend or family member to go through a mock interview with you. Be prepared ahead of time for questions that might be asked. To prepare for a phone interview, use the phone as much as possible ahead of time. Make the telephone a friend instead of your enemy as many stutterers have done.
If you can, get speech therapy from a therapist who specializes in stuttering. If you don't live close to one or can't afford it, try self-therapy.