The two privates, identified by their surnames Shin and Park, were both found hanged in their barracks on Sunday in separate locations near the heavily militarised border with North Korea, an army spokesman said.
Both men, who were in their early twenties, had been placed on a list of soldiers requiring special monitoring due to concerns over their mental stability.
The army spokesman said an investigation was underway in both cases.
Lim later told interrogators that he had snapped because he felt humiliated by the other soldiers, who mocked him and drew cartoons depicting him as SpongeBob Square Pants.
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Lim had also been listed as a soldier requiring special observation, and belonged to the same 22nd Infantry Division as Shin.
The South Korean armed forces rely heavily on a compulsory military service system, with conscripts -- most in their early twenties - accounting for the lion's share of its 690,000 active personnel.
Barrack-room bullying of fresh conscripts used to be rampant, and has been blamed for a number of suicides and shooting sprees in the past.
Tensions on the North-South Korean border have been running high in recent months, with North Korea conducting a series of ballistic missile tests.
"It's been going on for some time now, and soldiers have been under enormous pressure," Secretary General Lee Il-Woo of the private Korea Defence Network told AFP.
South Korea's low birth rate has cut the number of conscripts, and there are concerns that the army, in an effort to keep up numbers along the border, has been deploying soldiers who are not mentally suited to the pressures of front line duty.