Why does the water dissociation constant Kw remains constant? At $\pu{25 ^\circ C}$ at equilibrium the value of $K_\mathrm{w}$ is $\pu{1\times 10^{-14} M}$ and the concentration of $\ce{H+}$ and $\ce{OH-}$ is equal i.e. $\pu{1\times 10^{-7} M}$.
Now if we add $\ce{HCl}$ to it the $\ce{HCl}$ will form $\ce{H3O+}$ and so the concentration of $\ce{H+}$ increases and so the equilibrium shifts towards the left to counteract the changes. As a result the concentration of $\ce{OH-}$ decreases but why does still the $K_\mathrm{w}$ stays the same. If we add too much $\ce{HCl}$ such as 1 mole then we know it will completely dissociate and would form $\ce{H3O+}$ whose concentration would be $\pu{1 M}$.
So now what will happen to $K_\mathrm{w}$? Does it still remains constant but why? Does still the concentration of $\ce{H+}$ can not rise above $1\times 10^{-14}$ but why?
Your question reflects your knowledge in chemistry so I'll try to keep this explanation simple as possible.
Water conduct electricity because it contains $\ce{H+}$ and $\ce{OH-}$ ions by auto-ionization:
$$\ce{H2O &lt;=&gt; H+ + OH- \tag1}$$
It has been defined that this ionization is a constant at $\pu{25 ^\circ C}$. Thus by definition:
$$K_\mathrm{w} = [\ce{H+}][\ce{OH-}] = 1.0 \times 10^{-14} \tag2$$
Accordingly, by definition for pure water, $ [\ce{H+}]=[\ce{OH-}]= 1.0 \times 10^{-7}$. And then, there is a widely accepted principle in chemistry called Le Chatelier’s principle:

Le Chatelier’s principle is an observation about chemical equilibria of reactions. It states that changes in the temperature, pressure, volume, or concentration of a system will result in predictable and opposing changes in the system in order to achieve a new equilibrium state.

Accordingly, increasing the concentration of reactants (species on left hand side of the reaction) will drive the reaction to the right (more products), while increasing the concentration of products (species on right hand side of the reaction) will drive the reaction to the left (more reactants). At constant temperature, even though concentrations of species (e.g., here they are $\ce{H+}$ and $\ce{OH-}$ in equation $(1)$) at new  equilibrium state is changed, the equilibrium constant remains same. In other word, the equilibrium constant is depends only on temperature.
According to Le Chatelier’s principle, in in equation $(1)$, if you add more $\ce{H+}$ or $\ce{OH-}$ (RHS), the equilibrium would be adjusted to reduce that amount by making more water. But since this addition is at constant temperature, $K_\mathrm{w}$ remains constant.