If you remove "have", then it stops referring to a time that ends right now. It would relate to a time period which has already finished. "In the ten years I worked with him, I never heard him laugh". You no longer work with him, the time period has ended. It is possible that since you stopped working together, you have heard him laugh many times.
If the time period was ongoing, you would say "In the ten years I have worked with him, I have never heard him laugh". You still work with him.
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