Can I do an MBA with 2 years experience and no GMAT?

You will be glad to know that the answer to your question is a YES! While most top B-schools require a GMAT score, many other recognised business institutions consider your profile without a GMAT score for applying to their Business and Management program. Such universities usually focus on relevant hands-on experience in management or intense scholarly research that has mainly enhanced candidates' potential. So for many schools, a student's experience in management, the college's evaluation system, or relevant academic research keeps more weight than mere numbers obtained in a test.

Here is a list of US Universities offering MBA in the USA without GMAT:

Kenan-Flagler Business, the University of North Carolina, where the GMAT score is waived off, given the candidate submits an application requesting for the same, along with the required educational and professional transcripts, one month before the admissions process.
MIT Sloan School of Management, Massachusetts Institute of Technology, offers a 20-month-long Executive MBA program, making ten years of work experience mandatory for the application.
Questrom School of Business, Boston University, offers a Professional Evening MBA program, and waiver of a GMAT score lies at the sole discretion of the admissions committee.
Whitman, Syracuse University offers an Online MBA Programme that allows candidates to pursue this full-time course without relocating or even appearing for the GMAT, for that matter. Completed within 24 months, this is the best management program for qualified career-driven professionals.
Check out the Canadian Universities with no GMAT requirement:

Ivey Business School,Toronto, offers an Executive MBA program where one has to attend classes four consecutive days once every month and complete the course in 15 months, alongside their career. Although GMAT is not required, a well-detailed resume is mandatory for the application.
Sobey School of Business, Saint Mary’s University, offers a GMAT waiver in its Masters in Finance course, where applicants must submit the required transcripts after completing their four-year university degree course.
Lazaridis School of Business and Economics, Wilfrid Laurier University, offers a Part-time Alternate Weekend MBA that does not require a GMAT score, except for students who completed their undergraduate degree outside Canada.
Schulich School of Business, York University’s Executive MBA Program does not require a GMAT score, apart from valid academic credentials and other compulsory transcripts.
Let me know if you have any specific country in mind to pursue your MBA, or you can directly get in touch with Study Abroad Experts here.