Perhaps you are a
although I only have satisfactory explanations for four of those six lines:
Although in me you may find mistakes and misery
The letters of RULER contain (anagrams of) ERR and RUE. (Thanks to suomynonA for the hint in comments.)
I always measure up to what is expected of me
You use a ruler for measuring things.
You can use me to draw
You use a ruler for drawing straight lines.
I can also beat you raw
In the bad old days of corporal punishment, it was not uncommon for teachers to hit children with rulers. (Thanks to suomynonA for the hint in comments. D'oh!)
You may need me to plot the right way
Again, used for drawing, especially where accuracy is required as e.g. in plotting graphs or map routes.
Over people I hold sway
"Ruler" in the sense of king, queen, etc., now.
My (feeble) best guesses at the two lines I don't have good explanations for:
Mistakes and misery: (1) the word ends with -ER which sounds like ERR which means to make mistakes. Or (2) rulers not infrequently make mistakes and inflict misery on their subjects. Beating you raw: could again be a reference to the misbehaviour of autocratic rulers (who sometimes do worse to their subjects than just beating them).
But I find those unsatisfactory enough that I fear this answer may be only a clever red herring and have little to do with the intended one...