The abducted persons were, however, freed.
"There was a fierce encounter and under pressure from the security men, the Maoists left the four persons and fled," Superintendent of Police Kranthi Kumar told PTI over phone.
"One CRPF jawan (Badal Roy) died and 11 CRPF personnel and four Jharkhand Jaguars were injured in the blasts," a statement from the CRPF said.
Sources said a sub-inspector of CRPF lost his legs in the deadly attacks.
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The four were abducted on Saturday from near Navkania village situated in the foothills of Parasnath after Maoist intercepted their car, Kumar said, adding driver Rajendera was let off by the rebels.
The abducted persons were engaged in activities under social security pension and MG-NREGA, Giridih district officials said.
Helicopters were used to evacuate the injured personnel, four of whom are reported to be critically injured in the landmine blasts carried out simultaneously.