I have heard many physicists (ex:- Michio Kaku) saying "Warp speed" from Star Trek doesn't violate any known physical laws. But doesn't it violate causality? Say, we make warp drive possible and travel towards Alpha Centauri (4.22 light years away) in warp speed and reach there, say, within a year (+/- few months) and blow it up. Now using Special Relativity, we could devise a frame of reference wherein the observer would see the Star blow up before we ever left planet Earth. Wouldn't that violate causality and make warp speeds unattainable?
This is more of a meta answer, since it isn't really Physics, but it got a bit long to put in a comment. You say:
I have heard many physicists (ex:- Michio Kaku) saying "Warp speed" from Star Trek doesn't violate any known physical laws.
You need to think about precisely what this statement means. If we take the Alcubierre drive as an example it is a perfectly legitimate solution to Einstein's equation. So if General Relativity is a Law of Physics then the Alcubierre drive indeed doesn't violate any laws of physics, and it can be used to create closed time-like curves with the loss of causality that this implies.
But there are two problems with saying the Alcubierre drive doesn't violate any laws of physics:
Firstly the Alcubierre drive requires a ring of exotic matter to work, and exotic matter violates a number of energy conditions. If these count as laws of physics (and so far observation suggests they do) then the Alcubierre drive does violate laws of physics.
Secondly most of us believe that general relativity is an approximate theory that breaks down under a number of conditions (specifically in the quantum regime). It's been argued that when you take quantum effects into account a closed timelike curve causes an instability that destroys it. All this is speculative since we have no theory of quantum gravity, but if true it also means that the Alcubierre drive does violate laws of physics.
So when you see a bald statement like xxx doesn't violate laws of Physics, the statement is meaningless unless you specify the assumptions it is based on.
General relativity has several complications in regards to inertial frames, which I'm ignoring here because I think there's a more fundamental misunderstanding about special relativity and FTL going on here.
Now using Special Relativity, we could devise a frame of reference wherein the observer would see the Star blow up before we ever left planet Earth. Wouldn't that violate causality...?
No, it would not. The fact that you could devise such a frame is completely irrelevant to whether or not causality is violated. What's important is that nothing ever sends a signal to its own causal past, i.e. within or along its past light cone.
In general, an FTL signal of a fixed speed does not violate causality. To actually send something into your past light cone, you need FTL signals of at least two speeds in some particular inertial frame. That in some other frame you've sent a signal into the (coordinate) past doesn't matter. If you only ever use one particular FTL speed in one particular frame, no causal violations will occur.
Although physically restricting FTL to a single speed (again, in some particular inertial frame) would preserve causality, it would violate the principle of relativity instead, since there will be a unique, distinguished frame in which the signaling is instantaneous.
As for warp drives, we can take that as indication that a single warp bubble might or might not violate causality (depends on the geometry), but unrestricted ability to construct warp bubbles will surely enable us to violate it. This we can add to the many issues of constructing a warp drive.