Yes but it will not correct all of your myopia. Depending on your corneal thickness and the surgeons skill and experience and the instrumentation used about 6-8 diopters might be corrected. That however would make a huge difference in your vision without glasses and make your glasses much thinner.
I don't know if the information below from some doctors on the topic is the most current, but it appears surgeons vary in how much they treat. I suspect it depends partly on whether they have the latest equipment and use the latest techniques, and partly on how much risk they and the patient are comfortable with. As mentioned another option is to implant a lens, called a phakic IOL (IntraOcular Lens) or ICL (either standing for Implantable Contact Lens or Implantable Collamer Lens), and again surgeons will differ in their experience with them and their perception of the risks, some surgeons are inherently conservative, which merely means patients should educate themselves to decide whether to risk using a less conservative surgeon and getting a procedure done anyway since it is their risk to take if they are truly informed enough to decide to take it:
"Corneal excimer laser surgery — LASIK and advanced surface ablation techniques including PRK, LASEK and Epi-LASIK — is undoubtedly the most popular refractive surgical procedure performed in the pre-cataract population. It can accurately treat myopic refractive errors up to 12.00 D.
However, potential problems can crop up. ...
Phakic IOLs are a great option for myopes between -5.00 D to -20.00 D younger than age 40 years without cataract but with mild-to-moderate astigmatism. Additionally, PIOLs give us something for patients for whom LASIK and PRK are not appropriate. ...
Potential drawbacks of PIOLS ..."
"Some doctors consider -8 D to be the maximum, but in the United States the FDA has approved LASIK to treat up to -12 D....
Some patients with myopia of -10.5 D may choose to have an implantable lens (known as a phakic IOL) placed inside their eye as an alternative to LASIK.
The same complications are possible for a -10.5 D myope as for any other patient undergoing LASIK surgery. However, there will be a higher chance of needing a LASIK enhancement — a second, fine-tuning procedure — to obtain the best possible vision. — Dr. Caster...
A: The maximum treatment varies, based on several important factors, most prominently the thickness of the cornea. Different doctors have different criteria that they use when determining maximum treatment. For some doctors, 8 diopters of nearsightedness is the maximum, while others feel comfortable treating up to 12 or 14 diopters. — Dr. Caster"
This review suggests a phakic IOL may be the better choice:
"The results of this review suggest that, at one year post surgery, phakic IOLs are safer than excimer laser surgical correction for moderate to high myopia in the range of -6.0 to -20.0 D and phakic IOLs are preferred by patients"
This next article was updated this month and shows lasers approved by the FDA for up to -14D of myopia.
However how much can be corrected partly depends on details about your particular eyes, not everyone is a candidate. That said, that particular article doesn't say anything about the risks and outcomes. Again, often implantable lenses are recommended for high myopes, though there are risks (but then there are risks with wearing regular contact lenses for decades).
Hi, I am also suffering from myopia. I heard that the latest advancements in refractive surgery uses a technology called ReLEx SMILE (http://www.zeiss.com/meditec/en_de/products---solutions/ophthalmology-optometry/cornea-refractive/laser-treatment/femtosecond-laser-solutions/relex.html) developed by Zeiss. The surgical intervention is flapless and consists in removing a lenticular portion inside the cornea (in contrast to femto lasik and lasik that cut a flap and use the Excimer laser afterwards). The surgery can remove at most 10 spherical D and 5 cylindrical D of myopia, if the cornea permits. It also works for hyperopia.