Even if your monitor is 144Hz, it is recommended to disable vsync and run the game at a higher fps than 144fps (usually 500fps or higher is good enough). This is because the fps also affects the precision the game clients detects your input (in osu!lazer, the graphics fps is separate from the logic and input handling fps, so this wouldn't be the case anymore).
If this is configured correctly, you should see screen tearing while playing. The higher the fps, the more tears there are on the screen, but the smaller the difference between consecutive tears (so the effect is less noticeable overall). Having a screen with a high refresh rate also decreases screen tearing (144Hz is already on the high end of this, though).
As for reducing motion blur, you can try getting a better screen (though your screen is probably high end in this regard already).
You can also try to adjust the colors of your skin, screens usually have less ghosting when the pixels transition from dark-grey to bright-grey and vice-versa, compared to transitions from black to white (or very bright colors) and vice-versa, so you can try reducing the contrast between the notes and the background to reduce motion blur (note this actually can make things worse in some screens, if they employ some anti-ghosting techniques that can't handle this case well).
You can also try inverting the colors of your screen (so it is dark notes moving through a bright background, instead of the opposite), this might take a while to get used to, but it reduces the blur caused by vision persistence of your eyes. Reducing screen brightness overall also reduces blur by persistence of vision.