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#Java 7, 164 bytes

Java 7, 164 bytes

#Java 7, 164 bytes

Java 7, 164 bytes

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Kevin Cruijssen
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#Java 7, 164 bytes

String c(String a,String b){long s=x(b,1)-x(a,1)+(x(b,0)-x(a,0))*60,m=s%60;return(s/60)+":"+(m>9?m:"0"+m);}long x(String s,int i){return new Long(s.split(":")[i]);}

Explanation:

String c(String a, String b){       // Method with two String parameters and String return-type
  long s = x(b,1) - x(a,1)          //  Get difference in seconds from input times
           + (x(b,0) - x(a,0)*60,   //   plus the difference in minutes times 60 to get the seconds
    m = s%60;                       //  Temp variable of seconds after we've subtracted the minutes (used multiple times)
  return (s/60)                     //  Return minutes
    +":"                            //   plus ":"
    +(m>9?m:"0"+m);                 //   plus seconds (with a leading 0 if necessary)
}                                   // End of method

long x(String s,int i){             // Separate ethod with String and Integer parameters and long return-type
  return new Long(s.split(":")[i];  //  Return either minutes or seconds of String parameter based on the index
}                                   // End of method

Test code:

Try it here.

class M{
  String c(String a,String b){long s=x(b,1)-x(a,1)+(x(b,0)-x(a,0))*60,m=s%60;return(s/60)+":"+(m>9?m:"0"+m);}long x(String s,int i){return new Long(s.split(":")[i]);}

  public static void main(String[] a){
    M m = new M();
    System.out.println(m.c("0:00", "0:01"));
    System.out.println(m.c("0:55", "1:00"));
    System.out.println(m.c("1:45", "3:15"));
  }
}

Output:

0:01
0:05
1:30