Some additional context would help but with just what you have given I would take it to mean that the person being criticized isn't taking it seriously and the speaker is trying to impress upon said person that he is very serious indeed in his criticism.
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janajYou think maybe I am just sawing out a tune, when I say thisBecause the motion of drawing a bow across strings is similar to sawing a piece of wood, "sawing out a tune" could be a reference to "playing a violin". Playing a violin is often used as a metaphor for complaining or whining, possibly because solo violin music often accompanied sad scenes in si
I have heard that phrase one time and he used it to mean to exaggerate or overemphasize. I don't know if that fits but I hope this helps!