Deidara, a character from the Naruto Shippuden series, died by suicide bombing in his fight against Sasuke Uchiha. However, he failed to kill Sasuke with this explosion. This event is depicted in the Naruto Shippuden series [4] [6]. The anime does not provide explicit details on how other characters, such as Team Gai and Team Kakashi, escaped the blast radius [2]. It's possible that they used some kind of evasive maneuver or jutsu to avoid the explosion, but this is not shown or specified in the contexts provided.

Regarding the cause of Deidara's death, it was primarily due to his own character flaw - his obsession with art and his desire to fight Sasuke, despite the danger involved [3]. During the fight, Sasuke managed to slap Deidara, and Tobi's intervention with landmines only gave Sasuke more information, ultimately contributing to Deidara's defeat [7].

It's worth noting that Deidara's clay-based creations, including the one he used to kill himself, are known for their explosive properties [1]. However, the specific mechanics of how these creations work or how Deidara was able to survive previous explosions before his final fight with Sasuke are not explained in the contexts provided.