解:?$(1)$?∵?$A=x-\frac {1}{2}y+2$?,?$B=\frac {3}{4}x-y-1$?
∴?$A-2B=x-\frac {1}{2}y+2-2(\frac {3}{4}x-y-1)=-\frac {1}{2} x+\frac {3}{2}y+4$?
?$(2)$?∵?$3y-x=2$?,∴?$x-3y=-2$?
∴?$A-2B=-\frac {1}{2}x+\frac {3}{2}y+4=-\frac {1}{2}(x-3y)+4= -\frac {1}{2}×(-2)+4=5$?