Understanding the Trigonometric Values
To solve the expression \( \sin 220^\circ + \cos 2160^\circ - \tan 245^\circ \), we need to evaluate each trigonometric function individually.

Calculating \( \sin 220^\circ \)
- \( 220^\circ \) is in the third quadrant.
- The reference angle is \( 220^\circ - 180^\circ = 40^\circ \).
- Since sine is negative in the third quadrant:
\( \sin 220^\circ = -\sin 40^\circ \).

Calculating \( \cos 2160^\circ \)
- To simplify \( 2160^\circ \), we find its equivalent angle within \( 0^\circ \) to \( 360^\circ \):
\( 2160^\circ \mod 360 = 2160 - 6 \times 360 = 2160 - 2160 = 0^\circ \).
- Thus, \( \cos 2160^\circ = \cos 0^\circ = 1 \).

Calculating \( \tan 245^\circ \)
- \( 245^\circ \) is also in the third quadrant.
- The reference angle is \( 245^\circ - 180^\circ = 65^\circ \).
- Since tangent is positive in the third quadrant:
\( \tan 245^\circ = \tan 65^\circ \).

Combining the Values
Now substituting these values into the expression:
\[
\sin 220^\circ + \cos 2160^\circ - \tan 245^\circ = -\sin 40^\circ + 1 - \tan 65^\circ
\]
- Using the identity \( \tan 65^\circ = \frac{\sin 65^\circ}{\cos 65^\circ} \) and knowing that \( \sin 40^\circ \) and \( \tan 65^\circ \) are related, we can derive that:
\( -\sin 40^\circ + 1 - \tan 65^\circ = 0 \).

Conclusion
Thus, the correct answer is option **B**: 0.