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1.
When someone you are in a relationship with breaks up with you through a text. NO phone call or face to face, but a text dump.
Can you believe that jerk? He pulled a text dump. I knew I should have text dumped him when I had the chance.
by Jamie AKA The Hussy Housewife March 24, 2009
 
2.
Going to the bathroom (or other private place) exclusively to send/receive a text message. Usually to hide the fact that your texting someone other than the person/people you are with.
The boy I was on date with was lame, so at dinner I text dumped Sasha to see what she was up to when I ditched the loser.
by Lord Rader January 24, 2011
 
3.
The act of breaking up with a significant other via text messaging on ones mobile device.
I was at a bar when this stalker of a kid I was seeing showed up - I ignored him - two days later I text dumped him.
by Sarah1204 April 28, 2008