Why does Tsuna lose his clothes when infused with the Dying Will?
Anime often ignore real world's Physics laws. The losing of clothes on being infused with the Dying Will is used to dramatize the effect it has on Tsuna. It is to make you feel as if Tsuna's body "grows" when he receives the Dying Will, causing his clothes to rip apart.

Also, in a number of cases, receiving the Dying Will causes Tsuna to move from a lying down position to an upright position. This motion may also cause the clothes to rip, since they cannot "keep up" with the Dying Will.

Another explanation is that receiving the Dying Will is so intense that it tears or burns things in his immediate vicinity (which happen to be his clothes). I think this is a case of Rule of Cool in addition to Rule of Funny, and Fanservice could also be another reason.

The underwear remaining intact is for censorship reasons only. See Magic Pants.