It is Sunnat to trim the mustache so that there remains no hair over-lapping the upper lip. It is Mustahab (liked) to remove all the hair of the mustache. It is not Bid'at:
Extract from 'Daari Aur Ambiyaa ki Sunnat':
Trimming the moustache
Regarding the moustache five words have been used in the Hadith text:
- cut the mustache
- cutting the moustache
- shortening the moustache
- shorten the moustache thoroughly
- remove the moustache
Shaving the moustache has not appeared in any Hadith. 
For this reason, according to Imam Malik it is prohibited to shave the moustache.
"Many of the scholars of Kufa are of the opinion that to shave or remove the moustache completely is prohibited. Imam Malik also says this. He even says that one who does so should be disciplined. Imam Qasim narrates that Imam Malik was of the opinion that shaving the moustache is mutilation.
According to the Hanafi school of thought there is a verdict that regards the shaving of the moustache as a bidat (innovation).
"In Mujtaba it is mentioned that shaving the moustache is bidat."
There is also a second verdict according to the Hanafi School that regards shaving the moustache as a recommended act (Sunnah). Multaqi ul-Bahr has preferred this verdict. However, Allai in Durr Mukhtar has referred to this verdict as weak. In Mujtaba, Imam Tahawi is reported to have said that Imam Abu Hanifa, Imam Muhammad and Imam Yusuf also regarded shaving it as a recommended act (Sunnah).
The difference of opinion springs from the five words that have been narrated in the Hadith text. Two of these, and are used to show emphasis and this is achieved when shaving takes place. For this reason some scholars have ruled that it is recommended (Sunnah) to shave it. However, this is not so. If shaving was intended then the word is present in the Arabic language. Using another word instead of this word indicates that shaving is not desirable. Thus, the verdict of the Hanafi School of shaving being recommended (Sunnah) is not the preferred view.
The preferred view, according to the Hanafi School, can be divided into three:
- So much of the moustache should be cut so that the edge of the upper lip becomes apparent. Ibn Aabideen Shaami quotes from Mujtaba:
"The moustache should be cut so that it becomes equal to the upper edge of the upper lip. There is consensus that this is recommended (Sunnah).
It is recommended (Sunnah) to cut it so short that the redness of the upper lip becomes apparent. It should not be removed from the very root. The text of the Hadith which commands means precisely what has been mentioned above."
- So much should be cut that it becomes like the eyebrows. The author of Hidayah has written in At-Tajnis Wal Mazeed:
"It is preferred that so much of the moustache be cut that it becomes like the eyebrows."
Fataawa Aalamgiri has also prescribed this method.
- The entire moustache should be cut. Moulana Khalil Ahmad Sahib writes:
"All the five words indicate that the aim is to remove the hair completely.
Imam Tahawi mentions that he saw Muzani, the student of Imam Shafi, trimming his moustache and he also saw his own scholars doing so. Thus, the preferred view is that shaving the moustache is not an innovation (Bidat).
The recommended verdict (Sunnah) is to cut it thoroughly so that all the hair is short. Hadhrat Thaanwi has written that the preferred view according to some is to clip it thoroughly. Hadhrat Shah Sahib Kashmiri says that trimming it is better than shaving it. Thus, to thoroughly clip all the hair of the upper lip with a scissors is the preferred method. Sayyed Moulana Zakariyya Sahib says:
"A number of scholars of the past took the route that shaving the moustache is recommended (Sunnah). However, the research of the majority of the scholars is that it is recommended (Sunnah) to cut it. Cutting here would mean to thoroughly cut it so that it is similar to shaving it."
- To begin cutting the moustache from the right side is preferred.
- It is permissible to cut the moustache by oneself or allow someone else to do so. It has been narrated that the moustache of Nabi was cut by another person:
"Taariq Ibn Habib narrates that once a barber cut the moustache of Nabi . He saw a white hair
in the beard of Nabi and wanted to remove it. Rasulullaah caught his hand and said: 'A person who reaches any degree of old age then this will be a source of light for him on the day of Qiyamah.' "
Haafiz Badruddin Aini mentions in Umdatul Qaari, a commentary of Bukhari:
"A person has a choice regarding the cutting of the moustache. He may cut it on his own or allow someone else to do so since the purpose is fulfilled in both cases. However, one should not allow another person to cut the hair from beneath the arms and the pubic hair." (Aini)
In one edition of Nasai, the word does appear, but there is no guarantee regarding the chain of narrators.
Showkani, Naylul Awthor, Baabu Akhzish Shaarib
Allai, Durr Mukhtaar, vol. 5, p. 358, Bayaan Hazr Wa Ibaahah, Fasl fil Bai
Ibn Hajar, Nuqila Anhu fil Bazl, vol. 1, p. 33
Sayyed Thanwi narrated from him in At-Taraaif Waz Zaraaif
Ammal Halaq Fa Jaaizun Indal Ahnaaf Khilaafan Limalik (From : Imaali Shah Anwar Shah )
Khasaail Nabawi, Sharah Shamail Tirmidhi, p. 93
Mughni, vol. 1, p. 91