This paper deals with the critical blow-up and extinction exponents for the non-Newton polytropic filtration equation. We reveals a fact that the equation admits two critical exponents $q_1,;q_2;{in};(0,+{infty})$) with $q_1;{<};q_2$. In other words, when q belongs to different intervals (0, $q_1),;(q_1,;q_2),;(q_2,+{infty}$), the solution possesses complete different properties. More precisely speaking, as far as the blow-up exponent is concerned, the global existence case consists of the interval (0, $q_2$]. However, when q ${in};(q_2,+{infty}$), there exist both global solutions and blow-up solutions. As for the extinction exponent, the extinction case happens to the interval ($q_1,+{infty}$), while for q ${in};(0,;q_1$), there exists a non-extinction bounded solution for any nonnegative initial datum. Moreover, when the critical case q = $q_1$ is concerned, the other parameter ${lambda}$ will play an important role. In other words, when $lambda$ belongs to different interval (0, ${lambda}_1$) or (${lambda}_1$,+${infty}$), where ${lambda}_1$ is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely different properties.