Can somebody remove their bad karma by believing that it doesn't exist? If somebody does sin or bad karma, harms other living beings, but that person doesn't believe in karma and believes that karma is just an illusion. then how does his bad actions will harm him? For example, if I kill a mouse but I totally believe that nothing will happen, karma or religion is just people's belief, then will I ever be punished for that karma and such believe? Because there is also one saying that everything is just our belief? 

And also if I later ask for forgiveness to god for my bad karmas then will my bad karmas be forgiven?
You are expressing the stock definition of 'wrong view':

And how is right view the forerunner? One discerns wrong view as wrong
view, and right view as right view. This is one's right view. And what
is wrong view? 'There is nothing given, nothing offered, nothing
sacrificed. There is no fruit or result of good or bad actions. There
is no this world, no next world, no mother, no father, no
spontaneously reborn beings; no brahmans or contemplatives who, faring
rightly &amp; practicing rightly, proclaim this world &amp; the next after
having directly known &amp; realized it for themselves.' This is wrong
view... MN117

More graphically, it is described as:

There are some contemplatives &amp; brahmans who hold this doctrine, hold
this view: 'In acting or getting others to act, in mutilating or
getting others to mutilate, in torturing or getting others to torture,
in inflicting sorrow or in getting others to inflict sorrow, in
tormenting or getting others to torment, in intimidating or getting
others to intimidate, in taking life, taking what is not given,
breaking into houses, plundering wealth, committing burglary,
ambushing highways, committing adultery, speaking falsehood — one does
no evil. If with a razor-edged disk one were to turn all the living
beings on this earth to a single heap of flesh, a single pile of
flesh, there would be no evil from that cause, no coming of evil. Even
if one were to go along the right bank of the Ganges, killing and
getting others to kill, mutilating and getting others to mutilate,
torturing and getting others to torture, there would be no evil from
that cause, no coming of evil. Even if one were to go along the left
bank of the Ganges, giving and getting others to give, making
sacrifices and getting others to make sacrifices, there would be no
merit from that cause, no coming of merit. Through generosity,
self-control, restraint, and truthful speech there is no merit from
that cause, no coming of merit. MN60

You may choose not to believe in cosmic Karma, as in Hinduism, but kamma in Buddhism is only accrued due to intentional actions. Denying intention is denying agency, in one way or another. AN 3.61 deals with that issue, and with respect to God and kamma's place if God is to be believed in.
The Buddha did say:

Monks, these two are fools. Which two? The one who doesn't see his
transgression as a transgression, and the one who doesn't rightfully
pardon another who has confessed his transgression. These two are
fools.
These two are wise people. Which two? The one who sees his
transgression as a transgression, and the one who rightfully pardons
another who has confessed his transgression. These two are wise
people. AN 2.21

So confession is understood as wise, and acceptance of such is also, but this confession is to a human being.