If a black hole tears space time how can it still affect it's surrounding?

A black holes mass curves space far outside of its event horizon. You can feel it's gravity far away. Nobody knows what happens at the singularity. Relativity predicts all matter is squeezed to a point of zero size and infinite density. Gravity and spacetime curvature are infinite. But Relativity is not correct here because it doesn't take quantum mechanics into account. We need a quantum gravity theory. But nobody had figured that out yet. 

If you consider the idea of space-time being torn carefully, it becomes clear that it makes no sense.  There can't be a hole in space-time because a hole is a kind of space.  Black holes cause space-time to become very curved, which means effectively that the parallel postulate breaks down and parallel lines meet at a finite distance.

No one denies the singularity has no dimensions. It is a way of saying that the word "singularity" is something that cannot be analyzed or calculated. If we can't see, we can't know.

The pressure exerted onto matter in a black hole is so high that we simply don't see any light coming out of it. There are two types of black hole: stellar and supermassive. Stellar black holes are remnants of massive stars. They can have a diameter of a few kilometers. Supermassive black holes, on the other hand, are those found in the center of galaxies, and these can have diameters as large as our solar system and more with a mass million or billion times that of our sun.

How it can still affect its surroundings? Of course. Black holes attract anything close enough to their event horizons (the zone between the "hole" and the accretion disk.) Space-time is only the warping due to gravity; and it is everywhere.

It's not that simple. The laws of physics and quantum mechanics as we currently understand them break down at the event horizons of black holes. All data and  information disappear from THIS Universe and time become both zero and eternal because of the gravitational effects of the negative singularity that IS the black hole. It is not a literal hole or tear in the space time continuum, and NOT a "whole." Puns don't work very well and come across as insulting and provoking and condescending as well as revealing your ignorance of basic physics. 

A black hole affects is surroundings by its gravity and by its charge (if any).

The stuff inside the event horizon probably never actually reaches a "singularity" in a finite time due to time dilation and quantum effects.

"Tearing" of space time is really just a metaphor.

The Penrose singularity theorem says that under strong energy conditions (all geodesics converge rather than diverge), all time-like paths within the event horizon terminate at the same point - the singularity. It is not a hole, tear, or infinite - it is a termination point of spacetime paths.

A black hole presents three faces to the universe at the event horizon - mass/energy, electric charge, and angular momentum. These present the source of gravity to the external universe just as the surface area of the event horizons presents the entropy of the black hole and presumably the information content of the black hole.

Be aware that general relativity as a classical theory may simply fail at r=0, and likely needs to be replaced by a quantum gravity that may prevent singularities. Also be aware that the strong energy conditions of the Penrose theorem may be violated by torsion from quantum spins, pressure, or some completely unknown effect.