xyz SplitBy y then Drop y for ListLinePlot

This seems to be faster than the method in OP for large inputs:

TakeList[MyList[[All, {1, 3}]], Length /@ Split[MyList[[All, 2]]]]

 {{{1, 0.3}, {2, 0.4}, {3, 0.5}}, {{1, 0.7}, {2, 0.85}, {3, 0.9}}}

SeedRandom[1]
ml = RandomInteger[10, {100000, 3}];

nl1 = SplitBy[ml, Part[#, 2] &][[All, All, {1, 3}]]; // RepeatedTiming // First

 0.23

nl2 = TakeList[ml[[All, {1, 3}]], Length /@ Split[ml[[All, 2]]]]; // 
  RepeatedTiming // First

   0.057

nl1 == nl2

 True

If the input list is already ordered by the second column (as in the example in OP) you can also use GatherBy + Extract and GroupBy

SeedRandom[1]
ml = SortBy[#[[2]] &] @ RandomInteger[10, {100000, 3}];

nl1 = SplitBy[ml, Part[#, 2] &][[All, All, {1, 3}]]; // 
  RepeatedTiming // First

 0.22

nl2 = TakeList[ml[[All, {1, 3}]], Length /@ Split[ml[[All, 2]]]]; // 
  RepeatedTiming // First

 0.0073

nl3 = Extract[ml[[All, {1, 3}]], List /@ GatherBy[Range@Length@ml, ml[[#, 2]] &]]; // 
  RepeatedTiming // First

0.011

nl4 = Values @ GroupBy[ml, #[[2]] &, #[[All, {1, 3}]] &]; // 
  RepeatedTiming // First

 0.0065

nl5 = Values @ GroupBy[ml, (#[[2]] &) -> ( #[[{1, 3}]] &)]; // 
  RepeatedTiming // First (* the version from MarcoB's answer *)

  0.027

nl1 == nl2 == nl3 == nl4 == nl5

True

GroupBy[MyList, (#[[2]]&) -> (#[[{1,3}]]&)] // Values // ListLinePlot