First of all, you should apply Flags attribute to your enum. That will indicate that enum can be treated as a set of flags:
[Flags]
enum VectorAxis
{
    // Consider also adding value None = 0 when no axis ignored
    X = 1,
    Y = 2,
    Z = 4
}
Now you can use bitwise operators with enum values:
SampleMethod(VectorAxis.X | VectorAxis.Y); // pass both axis using bitwise OR
How does it work? If you take a look on the binary representation of enum values
X = 001
Y = 010
Z = 100
When you apply bitwise OR operation to X and Y (result has a bit set to 1 if any of values have a bit set to 1 on the same position) you'll get 011. And that's what will be passed to the method. In the method, you can check if the axis were passed using bitwise AND 
public void SampleMethod(VectorAxis ignoredAxis)
{
     if ((ignoredAxis & VectorAxis.X) == VectorAxis.X) // check using bitwise AND
        // X is ignored
}
The result of bitwise AND (you have 1 only when both values have a bit set to 1  on same position) of passed value 011 and value of X 001 gives you back value of X only when the corresponding bit is enabled in passed value.
011 & 001 = 001 // X is ignored
011 & 010 = 010 // Y is ignored
011 & 100 = 000 // Z is not ignored
Also instead of checking value manually, you can use Enum.HasFlag method which does the same
if (ignoredAxis.HasFlag(VectorAxis.X))