One of my dds was also prone to freaking out in frustration over any problem she didn't think she could do, although for her it happened most often with math. It is not easy to deal with - once she's upset, she's too upset to really come back around and work calmly, so for her, we just let her stop what she's doing and come back to it another day.
I may be old and grouchy, but to be honest, I can't see that being able to spell the level of words you've listed above (on a spelling test) is really necessary in 2nd grade, no matter how high a child's level of giftedness. If this were going on in my household, I probably would not make my child study the words if they were causing frustration. If the study session started out ok, I'd keep going for 5-10 minutes - but I'd stop there, and I'd stop on a dime if the frustration over spelling jumped back in. Unless he's in some type of situation where he has to make great grades to stay in a program, it just wouldn't be worth the hassle. I'd let my child focus on learning that's fun and in subjects he enjoys. Life is too short to have to spend 20-30 minutes studying spelling at home every night in early elementary!
polarbear