Sounds like it's time to take a deep breath and try a different tactic.
Spelling is very important. No one should rely on spell check as it does not catch everything, and how you present yourself on paper makes a big difference later in life.
Try taking some pressure off your son. Make the study time fun by creating puzzles or word finds. Set up a schedule where you study five words each night rather than trying to learn all of them at once. Have your son write the words three or five times each as part of the process.
Make the teacher your advocate rather than approaching her in anger. Tell her you are concerned about your son's spelling and ask for ideas on how to help him at home. Explain how frustrated he is. Don't make her feel that she is doing something wrong. Get on the same team so that your son benefits.
Find out how the bonus words really work. Can he choose to spell them? Are they words from previous weeks that he needs to remember? Obviously, if they are studying these words in class, your son knows what they are even if they are not on his spelling sheet. Can you ask him for the words so that you can study together?
And you might want to consider a different perspective. Most of us want our children to make straight As and learn easily. There is really nothing wrong with a B or a C. I have always had a different take. It's good to struggle a little and face a challenge. When your son has to stretch to reach his goals, you know that he is learning and developing. When grades and lessons always come easily, there is actually cause for concern.
Each year school is going to get a little harder. You don't want him to decide that when the going gets hard, the best thing to do is give up. What you want is for him t learn how to work smart.
The more creative you are in helping your son develop unique study strategies now, the better equipped he will be for middle and high school--and ultimately college and a career. Learning how to turn a challenge into an opportunity isn't just about school--it's a life skill that will set him apart!