In Blade Runner, did Pris's death imply that she was in some way mechanical/electrical?

The answer to this really is that "nobody knows", not for certain. Their composition changed with each telling.
Ridley Scott insists that they were biological, but their behaviour isn't that of a purely biological entity. There's a lot of grey area.

From Wikipedia - Replicant

In his novel Do Androids Dream of Electric Sheep? (the inspiration for Blade Runner), Philip K. Dick used the term android (or "andy"), but director Ridley Scott wanted a new term that the audience would not have any preconceptions about. As David Peoples was re-writing the screenplay, he consulted his daughter, who was involved in microbiology and biochemistry. She suggested the term "replicating", the biological process of a cell making a copy of itself. From that, either Peoples or Scott—each would later recall it was the other—came up with replicant, and it was inserted into Hampton Fancher's screenplay.

Although the press kit for the film explicitly defines a replicant as "A genetically engineered creature composed entirely of organic substance", the physical make-up of the replicants themselves is not clear. In the films's preamble, it is noted that replicants are said to be the result of "advanced robot evolution." The preamble also states that replicants were created by genetic engineers. Characters mention that replicants have eyes and brains like humans, and they are seen to bleed when injured. The only way of telling a replicant from a human is to ask a series of questions and analyze emotional responses, suggesting they might be entirely, or almost entirely, organic. The film also shows that at least certain body parts of a replicant are separately engineered and assembled, as shown with Hannibal Chew, a genetic engineer who specifically made replicant eyes. In a deleted scene, J.F. Sebastian was stated to have made replicant hands along with his own personal robotic toys.

Do Androids Dream of Electric Sheep? makes mention of the biological components of the androids, but also alludes to mechanical aspects commonly found in other material relating to robots. It states that the bone marrow can be tested to prove whether it is from a human or replicant.

In May 2012, Scott confirmed that the replicants were biological in nature, and contrasted them to the androids in the Alien series:

Roy Batty was an evolved... He wasn't an engine. If I cut him open, there wasn't metal, he was grown... and then within twenty years you get the first bill not passed in the Senate where they applied for replication of animals, sheep and goats and cattle and animals and they turned it down, but if you can do that, then you can do human beings. If you go deeper into it and say 'Yeah, but if you are going to grow a human being, does he start that big and I've got to see him through everything?' I don't want to answer the question, because of course he does... Ash in Alien had nothing to do with Roy Batty, because Roy Batty is more humanoid, whereas Ash was more metal.

As regards Pris' reluctance to 'just die'…

During the creation process of a replicant, their physical and mental capacities are separately ranked on a A to C system and designated for each replicant with the C level representing below normal human ability, B level being equal to a normal human and A being above normal human ability, the latter of which leads to superhuman physicality or genius level intelligence.

Pris was A-class physically…

Pris Stratton (played by Daryl Hannah) is referred to as a "basic pleasure model" for military personnel (Physical-A, Mental-B, N6FAB21416.)

Also from Wikipedia - List of Blade Runner characters

At an A-Physical Level, she is shown to have superhuman endurance (as in the scene where she grabs a boiling egg with her bare hand without harm) and an affinity for gymnastics.