Why is there blindspot for LIGO interferometer?

I am thinking maybe when the gravitational wave hits the 2 mirrors at the same time but the two mirrors are very far apart, so what could be the cause for the blindspot?

Nope. LIGO's principle of operation is to measure the difference of optical length between each arm (the optical length is the round-trip time of a light signal times the speed of light). As a gravitational wave passes through the detector, both of those lengths will vary and the variation of the difference of the lengths with time is then the signal measured by LIGO. Thus the blind spots are directions of propagations for the gravitational waves which induces, at any time, identical enough variations of length in both arms: the arm lengths change in step, so to speak.

To be a bit more specific, you first need to understand exactly how a gravitational wave passing through matter does modify lengths in different directions. You probably know that light waves can be polarised: the same is true for gravitational waves. As for light, there are several ways to express polarisation. One of them are the two polarisation called "plus" and "cross". Consider some massive beads on a ring and a gravitational wave passing through it, propagating perpendicularly to the plane of the ring. Then the "plus" polarisation will alter the ring as follow (credit: Wikipedia) whereas the "cross" polarisation will affect the ring as follow Then any gravitational wave is a priori the superposition of those two polarisations.

Now from that, I hope that you can intuitively see that no signal will result from a gravitational wave with either polarisation propagating along the line bisecting the two arms because both arms will be affected equally.