I found on some films that people are able to interrupt in the middle of animation and perform the combo. Example can be seen on these videos:
http://www.youtube.com/watch?v=wSxUiM4DNoQ&t=0h02m29s or in https://www.youtube.com/watch?v=aJROSP49_O8&t=0h04m43s ?

It's especially apparent with Heavy Naginata combo that is actually Whirlwind and then Spiral of death but in opposition to the videos when I tried it my character always had to complete Whirlwind animation and then start of Spiral of death, not before. Same can be seen with Axe Spear's Spin slash on second video - he stops left slash in the middle of animation and starts combo.

I, personally never made it and am thinking how is that possible?

A bit late here, but if you're still curious, pressing jump in the middle of the first animation (with no directions being pushed) and then doing the input for the follow-up move should let you interrupt it.