I have been a postdoc for a year and half with a good number of publications. I feel it is the time for seriously exploring the TT faculty positions. However, my mentor wants me to work for a few more years in the current position. Though I have good rapport with my mentor, I dont know if it is ethical and practically possible for me to proceed with applying without taking his reference. Advice will be appreciated.
It's your future and not that of your adviser, so I'm surprised that an adviser would say that they want you to work as a postdoc "for a few more years" -- which sounds far beyond the usual 3-year postdoc period.
My recommendation is essentially the same as for at least half of the questions on this forum: Communicate with your adviser. Have an honest talk about your future, why you desire to look for tenure track jobs, what you need from him in this regard, etc. You will very likely need your adviser's support (through letters, introductions, and in other ways), and the only way you'll get that is if you have honest conversations about what each of you want to get out of your current relationship.
Yes, it is ethical for you to seek a permanent position. And it is unethical for your advisor to hold you back. If s/he can provide you with a path to a more suitable position then it is less of a transgression. But preventing you from moving on is a serious breach.
The practical issue is harder. Your publication record may be enough without a strong letter. And if your advisor chooses to write a letter that subverts your chances then it is another very serious ethical breach. But someone reviewing your record can probably figure out the situation when there is a contrast between a strong publication record and record of productivity against a "sour grapes" letter of recommendation.
I suspect that your advisor has come to depend on you too much and hates to see you go, expecting a drop in productivity on their own part.
Some people will apply for a position and ask that the application be kept confidential in the short term until the institution starts to approach the decision stage. Most people will understand that such things are sometimes necessary for just the reasons you give here.