Electrons have very small mass and they are charged particles so they can be accelerated using strong electric fields. Also the mass of the electrons' mass will change significantly if it is accelerated to a speed comparable to the speed of light. Now I am wondering what will be the effect of that increased mass and that large speed. Will it be deadly ?
What will happen to you if I hit you with an electron after accelerating it to the maximum speed possible ?
As mentioned in the comments, although Special Relativity limits the velocity of particles, it doesn't limit their momentum or kinetic energy. So it's possible for a subatomic particle like an electron or proton to experience a high acceleration giving it a kinetic energy that would normally be associated with a macroscopic object.
The best-known example is the so-called Oh-My-God particle, a cosmic ray (probably a proton).
The Oh-My-God particle's energy was estimated as $(3.2 \pm 0.9) \times 10^{20}$ eV [with energy] equivalent to a 140 gram baseball travelling at about 26 m/s (94 km/h)!
However, such particles are rather rare (at least, they're rare in our part of the universe, thank goodness). There aren't many processes that can produce such prodigious accelerations, and any charged particle travelling through space is affected by electromagnetic fields and electromagnetic radiation, including the ubiquitous cosmic microwave background. This places limitations on the energy of cosmic ray particles, please see Greisen–Zatsepin–Kuzmin limit for details.
So what would happen to a human hit by such a particle? Not very much. It would pass through your body in a tiny fraction of a second, causing a little bit of damage to the cells it passes through. But our bodies have evolved to deal with such damage caused by cosmic rays and radioactive material in the environment, and they can easily handle small amounts of minor damage.
If you're unlucky, a cosmic ray may induce a mutation or cancer. But an ultra-high energy particle isn't really that much more dangerous than a more typical cosmic ray, apart from the fact that it's likely to hit more cells. Note that people living in high altitudes, or who spend a lot of time in aircraft or spacecraft get more cosmic ray exposure, and this does have a measurable impact on their probability of developing tumours; please see Health threat from cosmic rays for details. So it would not be good to be in a region where such high energy cosmic rays are common.
Getting hit by a beam of high energy particles is a far more serious matter. Russian particle physicist Anatoli Bugorski
is notable for surviving an accident in 1978, when a high energy proton beam from a particle accelerator passed through his brain. [...] On 13 July 1978, Bugorski was checking a malfunctioning piece of equipment when the safety mechanisms failed. Bugorski was leaning over the equipment when he stuck his head in the path of the 76 GeV proton beam. Reportedly, he saw a flash "brighter than a thousand suns" but did not feel any pain.
The beam passed through the back of his head, the occipital and temporal lobes of his brain, the left middle ear, and out through the left hand side of his nose. He received a dose of 200,000 to 300,000 roentgens. Bugorski understood the severity of what had happened, but continued working on the malfunctioning equipment, and initially opted not to tell anyone what had happened.
[...]
The left half of Bugorski's face swelled up beyond recognition and, over the next several days, the skin started to peel, revealing the path that the proton beam (moving near the speed of light) had burned through parts of his face, his bone and the brain tissue underneath.
As it was believed that he had received far in excess of a fatal dose of radiation, Bugorski was taken to a clinic in Moscow where the doctors could observe his expected demise. However, Bugorski survived, completed his PhD, and continued working as a particle physicist.
There was virtually no damage to his intellectual capacity, but the fatigue of mental work increased markedly.Bugorski completely lost hearing in the left ear, replaced by a form of tinnitus. The left half of his face was paralyzed due to the destruction of nerves. He was able to function well, excepting occasional complex partial seizures and rare tonic-clonic seizures.
That was caused by a high energy proton beam, with each particle having a tiny fraction of the Oh-My-God particle's energy.
