I have been trying so much to do this but to no avail. Some softwares like cooledit remove it to an extent but ruin other things in the music. Please suggest some good method for this.
As a friend of mine once explained, "It's like paint. If you mix together several colors of paint, you can't un-mix it and get the original separate colors of paint back."
Vocal removal software, as mentioned in other answers here, is only of limited usefulness due to laws of physics that cannot be circumvented. All such products use the principle of applying phase cancellation to a 2-channel stereo recording.
It is only possible to totally remove the lead vocal from a mixed recording using vocal removal software if the original recording is mixed under a precise combination of conditions: if the recording is 2-channel stereo, mixed with a wide stereo field, but the lead vocal is positioned exactly in the center, and there is no reverberation or echo applied to the lead vocal. Furthermore the process will always also remove any other instruments or musical elements that are also positioned in the exact center of the stereo field (where the bass instrument is usually positioned) so it is usually the case that removing the lead vocal also removes most of the bass instrument, the kick drum, and a great deal of bass frequencies at any point in the recording where the vocal removal effect is applied.
If the recording from which you wish to remove the lead vocal was not mixed according to these exact conditions, then you will encounter only a partial reduction in the volume of the lead vocal. If the lead vocal was processed with a stereo reverb effect, you might be able to remove the lead vocal but you will still hear the stereo reflections (echoes) of the lead vocal through the reverb effect. Regardless, you will probably notice undesirable artifacts and changes in the frequency spectrum.
Furthermore, the process of vocal removal won't work at all with mono recordings or, to the best of my knowledge, 5.1 or other configurations of multi-channel surround sound.
I basically asked this question on the Audio site: How can I cut out a particular instrument in the same pitch range as other instruments I don't want to cut?
As you can see there, the answer is no. There's no good way for software to tell what is voice and what is not for any arbitrary voice and song combined into a single waveform. As you note it can be done to an extent with varying effects on the song, but there is nothing that can do it very well yet.
The future is here. You can use a neuronal network called "spleeter" to separate voice and the arrangement of any song you like.
It is open source and can be freely downloaded from its official git repository: https://github.com/deezer/spleeter
I used it a lot and totally love it. The separation isn't 100% clean but it is still very good for hobby usage. For example for singing to original arrangement.
Maybe it is not that easy to install and run the programm for not programmers, since Spleeter do not have any graphical interface. But it is possible! Just follow the instructions on the git page and google or whatch youtube videos to clarify the single installation steps.
Have fun with it!
The only clean way to do this, assuming you don't have access to the pre-mixed individual audio tracks, might be to completely recreate the music without the vocal tracks. Perhaps try to transcribe the music and instrumentation extremely accurately (including all the subtile timing and pitch variations), feed this transcription to a midi synthesizer that has all the same instrument sounds, then play with a sound editor to tweak things until everything lines up with the original enough for your purposes. There might be research software that attempts to do some of this semi-automatically, not sure what state it's in.