jmc

We have $$1531_{12}=12^3+5\cdot 12^2+3\cdot 12+1.$$Note that $12^2$ is divisible by $8$, so $$1531_{12}=(\text{a multiple of 8})+3\cdot 12+1.$$Therefore, the remainder upon dividing $1531_{12}$ by $8$ is the same as the remainder upon dividing $3\cdot 12+1$ by $8$. This remainder is $\boxed{5}$.