Suppose there is a Sirius A based alien civilization, but their planet is heavily defended, so direct attack is useless. Could we use some kind of weapon to detonate the Sirius B and cause a disaster for that civilization?
No, not in any effective way Getting a star to explode requires masses on the order of solar masses. If you have the ability to move stars as weapons, you may more effectively use them as kinetic energy weapons.
A white dwarf is what's left when a star too small for a type II supernova runs out of fuel (our sun is in this category): it will go through a red giant phase, shed a fraction of its mass into a planetary nebula, then when fusion ends, shrink to a hot degenerate matter white dwarf (not heavy enough to form a neutron star).
If you have a white dwarf that's within years (or possibly decades) of a type Ia supernova explosion, it might be just possible to trigger the supernova early with a large enough compression event over a large enough fraction of the star's surface.
This kind of star is one that has collected hydrogen from a companion star over a long period, until the collected hydrogen (which lies on the surface of the degenerate matter stellar corpse) becomes deep enough for the lower layers to start to fuse; the reaction apparently occurs rapidly enough and symmetrically enough to push the remainder of the white dwarf into fusing elements like carbon and nitrogen, which in turn provides the energy to fuse iron and heavier elements (producing even trans-uranics, as happens in a classic type II supernova of a star of several solar masses), and the resulting energy literally blows the entire white dwarf apart, accelerating most of the mass beyond the star's escape velocity.
Triggering this kind of event early is a somewhat "hand-waving" situation, as it's not scientifically clear whether it's actually possible or what would need to be done. One method I'd suggest (as a thought experiment or plot device) would be to somehow bathe the entire surface of the star evenly in the correct variety of muons to trigger "cold" fusion in the surface layers (which are already plenty hot, just below fusion parameters), which would then compress the deeper hydrogen layers.
There might be other methods that would work, and are "easier" to accomplish, depending on the technology available. Bombarding the surface with anti-hydrogen or anti-protons, perhaps even a patterned application of very large fusion explosions would be enough if the star is close enough to the type Ia event.
If you're looking for an "explosive", a sufficiently large chunk of anti-matter will do nicely. If you're looking for something more exotic, I refer you Charles Stoss's Iron Sunrise
For this exercise, a field encompasses a volume of the star's core, and time is enormously sped up inside the field. Eventually, the volume becomes degenerate, and when the field is removed, with no radiation pressure to maintain the outer layers they free-fall into the center, then the collision produces a supernova.
Stross did rather finesse the question of what happened to all of the energy emitted during the "decay" process, but you can't have everything.