  With assumptions that the violation of the distance-duality (DD) relation entirely arises from non-conservation of the photon number and the absorption is frequency independent in the observed frequency range, we perform cosmological-model-independent tests for the cosmic opacity. The observational data include the largest Union2.1 SN Ia sample, which is taken for observed $D_\mathrm{L}$, and galaxy cluster samples compiled by De Filippis {\it et al.} and Bonamente {\it et al.}, which are responsible for providing observed $D_\mathrm{A}$. Two parameterizations, $\tau(z)=2\epsilon z$ and $\tau(z)=(1+z)^{2\epsilon}-1$ are adopted for the optical depth associated to the cosmic absorption. We find that, an almost transparent universe is favored by Filippis {\it et al.} sample but it is only marginally accommodated by Bonomente {\it et al.} samples at 95.4% confidence level (C. L.) (even at 99.7% C. L. when the $r<100 \mathrm{kpc}$-cut spherical $\beta$ model is considered). Taking the possible cosmic absorption (in 68.3% C. L. range) constrained from the model-independent tests into consideration, we correct the distance modulus of SNe Ia and then use them to study their cosmological implications. The constraints on the $\Lambda$CDM show that a decelerating expanding universe with $\Omega_\Lambda=0$ is only allowed at 99.7% C. L. by observations when the Bonamente {\it et al.} sample is considered. Therefore, our analysis suggests that an accelerated cosmic expansion is still needed to account for the dimming of SNe and the standard cosmological scenario remains to be supported by current observations. 
Cosmic opacity: cosmological-model-independent tests and their impacts   on cosmic acceleration