Does New Zealand's parliament have rules for expelling members?
Not the parliament. However, the parliament may suspend an MP and a party may expel a member.
Are there any parliamentary procedures which prohibit [indecorous language]?
That would appear to be covered under Standing Order 89, Disorderly conduct.
Can a bigoted remark ever result in the removal of a member of the parliament from their position?
It appears that the most that may be done, by the parliament, is suspension. However, the party may expel a member. Either, or both, will have some effect on the ability of the MP to represent their constituents.
STANDING ORDERS OF THE HOUSE OF REPRESENTATIVES
89 Disorderly conduct
(1) The Speaker may order any member whose conduct is highly disorderly to withdraw immediately from the House during the period (up to the remainder of that day’s sitting) that the Speaker decides, except that a member ordered to withdraw before or during oral questions may not return to the Chamber to ask or answer a question and no other member may ask a question on that member’s behalf.
(2) Any member ordered to withdraw from the House may not enter the Chamber but may vote.
90 Naming of member
The Speaker may name any member whose conduct is grossly disorderly and call on the House to judge the conduct of the member.
91 Member may be suspended
Whenever a member has been named, the Speaker forthwith puts a question, “That [such member] be suspended from the service of the House”. There is no amendment or debate on this question.
92 Naming in committee of the whole House
If a member is named in a committee of the whole House, the committee is suspended and the chairperson reports the matter to the House. The Speaker then puts the question for the member’s suspension as provided in Standing Order 91.
93 Time during which member is suspended
If any member is suspended under Standing Order 91, the suspension—
(a) on the first occasion is for 24 hours:
(b) on the second occasion during the same Parliament is for seven days, excluding the day of suspension:
(c) on the third or any subsequent occasion during the same Parliament is for 28 days, excluding the day of suspension.
94 Refusal to obey Speaker’s direction
If any member who is suspended under Standing Order 91 refuses to obey a direction of the Speaker to leave the Chamber, that member is, without any further question being put, suspended from the service of the House for the remainder of the calendar year.
95 Effect of suspension
(1) A member who is suspended from the service of the House may not enter the Chamber, vote, serve on a committee, or lodge questions or notices of motion.
(2) The Journals record the suspension of a member from the service of the House, and state the day or days on which the member is suspended from the service of the House.
96 House’s right to hold in contempt
The fact that a member has been suspended under Standing Order 91 or 94 does not prevent the House from also holding the member’s conduct to be a contempt.
There is also, under Standing Order 409, Contempt of House; however, no additional or separate penalties are given in the Standing Orders.
Chapter 8 Parties and Government
Expulsion from the parliamentary party
A party caucus may expel a member from membership. How it does so is a matter for it rather than the House. The leader of the party advises the Speaker of the change to its party membership, and the expelled member is thenceforth regarded as an independent member.