Bloontonium Saboteur assists in limiting Bloontonium of the opponent, suppressing their defensive capabilities. 4 lost Bloontonium may seem minor, but for certain Heroes it's a big deal-breaker.
For Adora's Sun Shield, it can prevent one or two Sun Shields depending on Adora's Bloontonium (e.g. dropping from 14/15 Bloontonium prevents two Sun Shields, or one with 15/15).
Obyn Greenfoot control decks tend to equip few Bloon cards in their deck, since they'd only focus on having just enough Bloontonium to unlock Nature's Shield.
Zee Jay OTK decks often keep their Bloontonium at 10 if they are preparing for an OTK with Rad Bloon. Playing BSabo at the right moment can force enemy Zee Jay to play more Bloons to get back to 10 Bloontonium.
This card is generally outclassed by Haunting Night as a Bloontonium drainer, which is slightly more expensive but drains a lot more Bloontonium and gives the Bloontonium to the player. While this card also has some damage output after playing it, it isn't very useful against the control and Zee Jay OTK decks that Bloontonium drain is used for.
When playing against this, simply use all your Bloontonium, making its On Play effect useless. Or cancel out the effect next turn by having Bloontonium production; 1 Mine Supervisor and 2 Bloontonium Miners, or two Mine Supervisors, give the same amount.
Some Heroes, especially Adora, may depend on Bloontonium during the opponent's turn.
Bloontonium Saboteur is the only Military Monkey other than Mortars to have 1 delay. This is significant for Striker Jones, as it opens opportunities for his Orders Received and War Bonds.