There is no way to programmatically disable a trigger temporarily. Note that you can disable triggers on the server command line using the -gf command line option (but this is not going to help you here).

One method that may solve your problem is to let the trigger fire but programmatically make the operation a no-op. One method to doing this would be to wrap the logic within your trigger code with, say, a test of a connection variable.

For example:

CREATE TRIGGER myTrig AFTER INSERT
REFERENCING NEW as new_name
FOR EACH STATEMENT
BEGIN
   DECLARE @execute_trigger integer;
   IF varexists('enable_trigger_logic') = 1 THEN
      set @execute_trigger = enable_trigger_logic;
   ELSE
      set @execute_trigger = 1;
   END IF;
   IF @execute_trigger = 1 THEN
      ... <your-trigger-code-goes-here>
   END IF;
END;

Note that my example checks that the global connection variable exists before attempting to use the variables value. The non-existing variable implies that triggers are enabled.

Then when you want to disable the triggers temporarily, you would do:

   ...
   IF varexists('enable_trigger_logic') = 0 THEN
      create variable enable_trigger_logic int;
   END IF;
   set enable_trigger_logic = 0;
   ... < execute-your-code-that-you-do-not-want-triggers-to-run >
   set enable_trigger_logic = 1;
   ... < now-your-trigger-code-will-do-its-work >

If you were going to do this a lot, you could create two procedures and one function:

CREATE PROCEDURE sp_disable_triggers ()
BEGIN
       IF varexists('enable_trigger_logic') = 0 THEN
          create variable enable_trigger_logic int;
       END IF;
       set enable_trigger_logic = 0;
END;

CREATE PROCEDURE sp_enable_triggers ()
BEGIN
       set enable_trigger_logic = 1;
END;

CREATE FUNCTION f_are_triggers_enabled ()
RETURNS INT
BEGIN
       IF varexists('enable_trigger_logic') = 1 THEN
          return enable_trigger_logic;
       ELSE
          return 1;
       END IF;
END;

Now you can use:

call sp_disable_triggers();
... <execute-your-code-where-trigger-logic-is-disabled>
call sp_enable_triggers();
... <execute-code-where-trigger-logic-will-run>

and within your trigger use:

IF f_are_triggers_enabled() = 1 THEN
     ... your trigger logic
END IF;

Note: If you are using a row level trigger then you can add a WHEN clause containing the condition and leave the trigger code as is. ( Thanks to TDuemesnil for making this suggestion! )