Slump block is a concrete masonry unit with a rounded, rustic finish that is made to resemble mud adobe. I talked with a slump block manufacturer about your question and they referred me to Prosoco Inc.
Prosoco’s products have been used to clean some very high-profile buildings, including the U.S. Capitol and the London Stock Exchange. When I posed your question to one of Prosoco's customer service representatives, he asked if this was going to be used by a homeowner.
If that’s the case, the strongest thing they could suggest would be a general-purpose, non-etching acidic cleaner followed by a penetrating, breathable water repellent. Prosoco's two products for this would be their Light Duty Concrete Cleaner and Siloxane WB Concentrate, both sold under the Sure Klean brand name.
The latter is solvent-free and made to be diluted with water; you can spray it on or brush it on. The former, even though it is called light duty, is a formulation of hard-working chemicals, so be sure to read the instructions and follow them carefully. For example, you'll have to cover windows and doors with polyethylene to protect them from the cleaner. Other non-masonry surfaces should be protected as well.
If the slump block requires more heavy-duty cleaning, contact a concrete and masonry restoration professional, who should have access to heavy-duty solutions for chemical cleaning, as well as expertise in using them.
Prosoco products are sold primarily to professionals through masonry supply houses. More information is available at www.prosoco.com.