When you remove the monitor it will alert the authorities.
If you go "on the run" a directive (warrant) will be issued to pick you up and you will be found and placed in detention. You would be wise to reconsider this decision and contact your probation officer to see what other options the 2 of you can come up with before you dive into deeper trouble. If things are difficult at home, the P.O. May be able to work out an alternative place for you to stay. It doesn't hurt to explore the possibilities! Good luck.
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You will go to detention if you cut off your monitor. You could go to the Texas Youth Commission. When you turn 17 you go to adult jail. You don't want to go to either of those places. If you run you better hope they catch. At 16 with no money you could easily wind up dead or abused. It's not worth it. I've been doing criminal law for 20 years and I hate seeing people throw away their life. Get help.
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Vicky and Richard are both right. I practice in El Paso before the Juvenile Courts and can tell you that the worst thing you can do now is run. WHEN they catch up to you the Judge will have every option open to him including TYC until you are 21 years old. If you are 16 now then that means up to 5 years in TYC. Go see your PO and try to work it out. The Judge's are hard but they are fair. It may not seem like it now but they want what's best for you and to keep you out of the adult system. That is somewhere you do not want to be.