The world number one responded to a post on Instagram that described the American as "very average".
Spieth replied: "Couldn't be further from the truth troll. Go do research before hating."
Defending champion Spieth bogeyed five of his first seven holes to trail the leaders by seven strokes on two over.
The 22-year-old shot 30 under par to win the Hyundai Tournament of Champions in January but his form has slumped recently, with a missed cut in the Northern Trust Open followed by a 17th-place finish in last week's WGC-Cadillac Championship.
World number two Rory McIlroy backed his rival, posting on Twitter: "No, he's not TW (Tiger Woods), he's not slumping and he's not done. He's a double major winning 22 year old. He'll be just fine!!"
Spieth, 22, also took exception to a post on the PGA Tour's official Twitter account that he thought used one of his remarks out of context.
It highlighted a joke from the his post-round interview when asked whether he could accept having an occasional off day.
The PGA post, later deleted, read: "What good is kicking the door other than hurting my foot and [having to] withdraw?"
Spieth responded: "Seriously? That's the quote you're going to use out of that article?"
He later explained: "I was a little upset. It made it seem like I was OK with getting hurt and withdrawing. I was frustrated with that."
There were signs of encouragement for the Masters and US Open champion after his dreadful start as he recovered for a second round of 68, two shots inside the cut.
"Today was all about the cut," he said.
"I actually did pretty well to make six [at the first hole]. I thought it was really strong what we did after that. For the first 20 holes to be at six over and we finished at two over, [there are] only positives going forward."
Steve Stricker holed a 150-yard shot for an eagle two in a 66 as he moved into the joint lead on five under with fellow American Will Mackenzie (67).
They lead compatriots Daniel Berger (68) and Bill Haas (67), and Canada's Graeme DeLaet (66), by one stroke.
England's Danny Willett is level par after a one-over 72, while Ian Poulter is one over after a level-par 71 and Scotland's Russell Knox improved to to two over with a 69.
Luke Donald joined Knox after also firing a two-under 69.
However, Northern Ireland's Graeme McDowell (72) and Martin Laird (75) were among those who missed the cut.
Jordan Spieth defended himself after being called "garbage" by an internet "troll" as he narrowly made the cut at the Valspar Championship in Florida.