解:$(1)A+3B=-x-2y-1+3(\frac {1}{2}x+y+1)$
$=-x-2y-1+\frac {3}{2}x+3y+3$
$=\frac {1}{2}x+y+2$;
$(2)$将$x+2y=6$代入,得
$A+3B=\frac {1}{2}(x+2y)+2=3+2=5$
$(3)$即$A+mB=-x-2y-1+m(\frac {1}{2}x+y+1)$
$=(\frac {m}{2}-1)x+(m-2)y+m-1$的值与$y$无关
则$m-2=0$
得$m=2.$