Is it possible to become totally envy free? Can we develop a particular mind set for being totally envy free; to stop envying others?
Smith and Kim's (2007) review article in the prestigious Psychological Bulletin titled "Comprehending Envy" might be a good starting point. They define envy as


  an unpleasant, often painful emotion characterized by feelings of
  inferiority, hostility, and resentment caused by an awareness of a
  desired attribute enjoyed by another person or group of persons.


They are also clear to distinguish proper envy from several other emotions including benign envy, longing, jealousy, and resentment.

Individual differences in experiencing envy: As a starting point, from a trait personality perspective, people differ in their tendency to experience various emotions. In particular neuroticism is associated with a tendency to experience negative emotions. Smith and Kim (2007) mention several self-report scales:


"Dispositional envy scale (DES; R. H. Smith, Parrott,Diener, Hoyle, &amp; Kim, 1999) consists of eight items, four of which ask respondents to indicate the degree and frequency of their
experiences of envy"; copy of items
"measure of enviousness developed by Gold (1996) uses a number of items containing familiar idioms that were argued to encourage truthful responses."


Table 2  from Smith et al (1999) report the means and SDs for the items of the DES. The means and sds are generally less than 2.5 on a 1=strongly disagree to 5=strongly agree scale (e.g., I feel envy everyday M=2.3).
This  suggests that a bit over half the participants are either disagreeing or strongly disagreeing with the test items.
The scale showed moderately strong positive correlations with neuroticism and negative correlations with self-esteem. Thus, you might conclude that some people rarely consciously experience envy. That said, some researchers consider that this might be due to social desirability in responding or even at a deeper level, people may not even realise that they are experiencing envy.

Thus, while social desirability might explain some of the individual differences, I think that some people just rarely experience envy. That said, this still leaves open the question of how people who do experience negative effects from envy, might reduce such effects.

Coping with envy:
Smith and Kim (2007) review research on coping with envy:


  Types of strategies for coping with envy. Salovey and Rodin (1988)
  followed up their survey by examining what strategies people use to
  cope with envy and jealousy and to assess which seemed most effective
  in doing so. Participants completed a questionnaire assessing their
  emotional reactions to envy-provoking situations in a number of
  domains and the frequency with which they used three distinctive
  coping strategies (self-reliance, selfbolstering, and selective
  ignoring). A number of important, suggestive findings emerged.
  Self-reliance, which included items tapping emotional control (e.g.,
  “refrain from feeling angry”), perseverance (“don’t give up”), and
  goal commitment (e.g., “become committed to the goal”), and to a
  lesser extent, selective ignoring (“decide it isn’t so important”)
  were associated with reduced envy. Self-bolstering (e.g., “think about
  my good qualities”) was unrelated to reduced envy; however, for those
  participants already experiencing envy, it was associated with less
  depression and, along with self-reliance, with less anger, both
  affects associated with the experience of envy. Salovey and Rodin
  (1988) interpreted these findings to mean that the more effective
  strategies for reducing initial envy appear to be stimulus focused rather than
  self-focused.


References


Smith, R. H., Parrott, W. G., Diener, E. F., Hoyle, R. H., &amp; Kim, S. H. (1999). Dispositional envy. Personality and Social Psychology Bulletin, 25(8), 1007-1020.
Salovey, P., &amp; Rodin, J. (1988). Coping with envy and jealousy. Journal
of Social and Clinical Psychology, 7, 15–33.
Smith, R. H., &amp; Kim, S. H. (2007). Comprehending envy. Psychological bulletin, 133(1), 46. PDF