Is there a way in beast mode to split a column by a common character?

You would need to combine the INSTR,SUBSTRING, and LENGTH functions to do this in a beast mode.

With that being said, I STRONGLY ADVISE AGAINST DOING THIS IN A BEAST MODE.

But you asked if it was possible... and it is... but it causes what seems to be A LOT of validation time on my 4 line dataset consisting of the following values:

abc.123.xyz.789 
argh.zoom.yak.melt
apple.banana.cherry.42
1.2.3.4

Field 1 (seemed simple enough, lets go!)

SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1)  -- SUBSTRING(`COLUMNWITHDATA`,[STARTING POSITION],[STRING LENGTH])
						   -- Starting Position = 1 (first character)
                                                   -- String Length = Position of first period character
                                                   -- -1 as we must consider the first period character and backup one character

Field 2 (here's where you start to get the idea... of why this is a bad idea... I tried commenting this out to make it easier to follow... but I admit I may have failed to do so in the endeavor)

SUBSTRING(
SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1)))
,1
,INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.')-1
)
-- CONSIDER FIELD1:
-- SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1) -- SUBSTRING([STRING],[STARTING POSITION],[NUMBER OF CHARACTERS])
												     -- Starting Position = 1 (first character)
                                                     -- String Length = Position of first period character
                                                     -- -1 as we must consider the first period character and backup one character
-- FIELD2:
-- SUBSTRING(		-- this SUBSTRING, is what I will refer to as SUBSTRING1
-- first parameter of SUBSTRING1 begins:
-- SUBSTRING(`_COLUMN_1`,		 -- FIRST PARAMETER of SUBSTRING2 - [STRING]='abc.123.xyz.789'
-- INSTR(`_COLUMN_1`,'.')+1,	 -- SECOND PARAMETER of SUBSTRING2 Field1 add 1 (find the period, shift right one position) [STARTING POSITION]=5
-- LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1)) -- THIRD PARAMETER of SUBSTRING2 Find length of [STRING] and subtract the length of Field1, to return the length of the remainder of [STRING].. [NUMBER OF CHARACTERS]=11
-- first parameter of SUBSTRING1 ends, so now SUBSTRING1 has [STRING]='123.xyz.789'
-- second parameter for SUBSTRING1 begins:
-- 1, -- We're starting at position one, of '123.xyz.789'
-- third parameter of SUBSTRING1 begins
-- EDITOR'S NOTE: we have to find the length of '123' but we have to find it from 'abc.123.xyz.789' because we can't store '123.xyz.789 in a variable, which would make this tremendously easier.
-- INSTR(  		-- NEED TO FIND THE POSITION OF the first period in '123.xyz.789' so first we have to return 123.xyz.789 with SUBSTRING3
-- SUBSTRING(`_COLUMN_1`, -- FIRST PARAMETER of SUBSTRING3 (abc.123.xyz.789)
-- INSTR(`_COLUMN_1`,'.')+1, -- SECOND PARAMETER of SUBSTRING3 [STARTING POSITION]=5
-- LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))) -- THIRD PARAMETER OF SUBSTRING3 [NUMBER OF CHARACTERS]=3 -- whole string length (15), minus the length of Field1 'abc' gives us 12
-- ,'.') -- FIND THE POSITION of the first period in '123.xyz.789'
-- -1 -- subtract one more length character, for the period delimiter gives us 11
-- Third parameter of SUBSTRING1 ends [NUMBER OF CHARACTERS]=3
-- ) -- END SUBSTRING1

Field 3 (note that explanations/comments have disappeared entirely at this point...)

SUBSTRING(
	SUBSTRING(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),
    INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.')+1
    ,LENGTH(`_COLUMN_1`)-LENGTH(INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.'))
             )
  ,1
  ,INSTR(SUBSTRING(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),
          INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.')+1
          ,LENGTH(`_COLUMN_1`)-LENGTH(INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.'))),'.')-1
         )

Field 4 (Still no comments... I hope just by looking at Fields 3&4 it becomes clear why SUBSTRING_INDEX is a function that was created so people like me wouldn't write things like this)

SUBSTRING(
	SUBSTRING(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),
    INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.')+1
    ,LENGTH(`_COLUMN_1`)-LENGTH(INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.'))
             ),
			 INSTR(SUBSTRING(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),
          INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.')+1
          ,LENGTH(`_COLUMN_1`)-LENGTH(INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.'))),'.')+1,
			 LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),
    INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.')+1
    ,LENGTH(`_COLUMN_1`)-LENGTH(INSTR(SUBSTRING(`_COLUMN_1`,INSTR(`_COLUMN_1`,'.')+1,LENGTH(`_COLUMN_1`)-LENGTH(SUBSTRING(`_COLUMN_1`,1,INSTR(`_COLUMN_1`,'.')-1))),'.'))
             ))-1
         )

Here is a card with my exampled dataset output:

Hopefully this is of help to you in understanding your challenge. I would strongly suggest using the SUBSTRING_INDEX function in an SQL dataflow.  Use these beastmodes at your own risk, as even on my minimal test data they seem to validate/process quite intensively, can't imagine it would go well if you pointed these at a large dataset.