Is there any way to avoid wasting a long time in review process for mathematics journals?
Are there journals with fast reviewing process?

The really quick ones are the "questionable" journals ... every paper is accepted, and published (for a hefty fee).

The Notices of the American Mathematical Society publishes a survey once a year, which includes information on mathematics journals, including statistics on time from submission to publication (when available).

added  

"Backlog of Mathematics Research Journals"
Notices of the AMS, Volume 61, Number 10,
November 4, 2014, page 1268.