Be the death of is generally used as an exaggerated or humorous way of describing the effects of laughter, embarrassment, boredom or similar emotions.
1999 - Chris Dolan - Ascension Day - If her mother ever found out that William Grant was in Glasgow, it'd be the death of her.
RELATED IDIOMS :
at deaths door = at death's door
so ill that you may die
1994 - S. P. - Somtow Jasmine Nights - How stupid of me to trouble her with my petty problems when she's probably at death's door!
be frightened to death
be made very alarmed and fearful - informal
be in at the death
be present when a hunted animal is caught and killed
be present when something fails or comes to an end
catch your death = catch your death of cold
catch a severe cold or chill – informal
a deaths head at the feast = a death's head at the feast
A naked human skull as the emblem of death
the head of the conventional personification of death
I had rather be married to a death's-head with a bone in his mouth.
die a death = die the death
come to an end
cease or fail to be popular or successful
1999 - Linedancer - Our industry must expand otherwise it will die a death with just a few clubs remaining.
do something to death
perform or repeat something so frequently that it becomes tediously familiar
a fate worse than death
a terrible experience, especially that of seduction or rape
1991 - Thomas Hayden - The Killing Frost – He dominated the conversation, holding the Hackett and Townshend women spellbound as he told of how he had broken up a white slave ring in Dublin, and how he had rescued an innocent young girl from a fate worse than death.
like death warmed up
extremely tired or ill – informal
Like death warmed up was originally military slang recorded from the 1930s. The North American version is like death warmed over.