Is there any procedure that we can associate one defect with multiple test cases without any duplications in Test Director 8.0.

To find duplicate defects click on Defects Tab and then select the defect for which u r looking for duplicate. After selecting/highlighting click on the find similar defects button on top then Similar Defect Dialgo box opens with the percentage of detected similarity. Like this u can find if theres any duplicate.

There is no certain procedure to Associate Same defect to different test cases, you could Give the comments in the failed test case, stating that the test case failed due to the Defect ID.