You can find list of tiebreakers in Wikipedia article on 2018 FIFA World Cup (link to the current revision). They are specified in Section 32.5 of 2018 FIFA World Cup Regulations (link to Internet Archive) and on FIFA World Cup site (Internet Archive). I have also copied them below.
If I understood them correctly, this is what happens in the situation described in your question.
As you rightly point out, in this scenario the first three tie-breakers (i.e., points, goal difference, goals scored) will not decide anything, since the three teams have exactly the same score.
Germany | 3:2 | 6
Mexico | 3:2 | 6
Sweden | 3:2 | 6
S.Korea | 1:4 | 0
The next criteria are points, goal difference, goals scored in the matches between the tied teams. So we look only at these matches, which are: GER-MEX 0:1, GER-SWE 2:1, SWE-MEX 1:0. Now if we make table just from these matches we get
Germany | 2:2 | 3
Sweden | 2:2 | 3
Mexico | 1:1 | 3
We see that Germany and Sweden are tied, Mexico is eliminated. So Germany and Sweden advance further, but the group winner is still not decided.
The next tie-breaker are fair-play points which take into account yellow and red cards. After two matches Sweden is ahead of Germany. (Which is not surprising, considering that the Boateng's red card from the match against Sweden is at the moment the only red card in this group.) But this can change after the remaining matches.
If they are tied even on fair-play points, then the team who advances further is decided by drawing lots.
I will add that there already are a few related questions (and answers) on this site. For example:
The only difference between 2014 and 2018 World Cup tie-breakers is the addition of fair-play points.
Remark. The question whether after eliminating Mexico we should apply the same criteria again to the remaining teams - Germany and Sweden - keeps popping up in the comments. It is true that this is often done in groups stage of various competitions. However, it seems that in such cases it is explicitly mentioned in the regulations. (For example, 2017-18 UEFA Champions League's tiebreaker rules explicitly say that: "If more than two teams are tied, and after applying all head-to-head criteria above, a subset of teams are still tied, all head-to-head criteria above are reapplied exclusively to this subset of teams.") Since here the regulation do not say so, I followed explicitly what is written there and did not apply d), e), f) again to the match between Sweden and Germany.
I have no problem to admit that the rules are a bit ambiguous. It is not surprising that many other sources discuss the situation and possible scenario. And some of them put Germany ahead on Sweden based on their match. For example: Germany World Cup scenarios, tiebreakers: How the defending champs, rest of Group F can advance (CBS Sports) or If Sweden beats Mexico 1-0 and Germany beats South Korea 1-0 ... (Reddit), World Cup group permutations: Who can qualify for the Round of 16? (ESPN).
I will also add a link to this page: http://webhome.csc.uvic.ca/~haron/FIFA/index.html and also http://webhome.csc.uvic.ca/~haron/FIFA/scenarios.html - which also points out some ambiguity in the rules. It seems that the author of the website in fact contacted FIFA in connection with this. (It was during 2010 World Cup, but the rules were similar.) Here is a quote from that page:
Which one of these two interpretations is correct? When reached via email, the FIFA Media Department replied that There's a three-way tie to break. You do it as a one operation and not in different stages. The teams concerned are always all the teams involved in the tie-break. In other words, the FIFA Media Department interpreted the teams concerned to be all three teams. However, when Canadian Soccer Association's Director of Referees Joe Guest was presented with this scenario by the Times-Colonist, he interpreted the teams concerned to be USA and England. Thus, the two parites differed on whether USA or England would advance.
EDIT: I have mentioned this in comment, but probably it's better to add it to answer so that it is visible a bit better. As pointed out by Labba's answer, this is now clarified on the 2018 FIFA World Cup website and it explicitly says that in the hypothetical scenario here, the fair-play points would decide between Germany and Sweden. As far as I can tell, this information was not given there at the time when I posted this answer. (Compare the snapshots from June 24 and from June 25.)
Here is the copy of the relevant section from the 2018 FIFA World Cup Regulations:
The ranking of each team in each group shall be determined as follows:
a) greatest number of points obtained in all group matches;
b) goal difference in all group matches;
c) greatest number of goals scored in all group matches.
If two or more teams are equal on the basis of the above three criteria, their rankings shall be determined as follows:
d) greatest number of points obtained in the group matches between the teams concerned;
e) goal difference resulting from the group matches between the teams concerned;
f) greater number of goals scored in all group matches between the teams concerned;
g) greater number of points obtained in the fair play conduct of the teams based on yellow and red cards received in all group matches as follows:
– yellow card: minus 1 point
– indirect red card: minus 3 points (as a result of a second yellow card)
– direct red card: minus 4 points
– yellow card and direct red card: minus 5 points
Only one of the above deductions shall be applied to a player in a single match;
h) drawing of lots by FIFA.