Ok, go to "Tools" section of the site and download "Warcraft 3 Model Editor"
Install/Extract it, go to your Warcraft 3 folder and open the war3.mpq file with the editor (right-click the file and then click "Open with War3 Model Editor"), find the unit .mdx file you want to remove the animation and export (right-click on the file "Export as..."), now procced to the exported file and open it with War3 Model Editor (double click it), while in the editor, click "Windows -> Sequence Menager", find the animation you want to remove, right click on it and click "Remove", then save the file, import it into the map you want - you are done.