Industrial solid waste has been widely used as an alternative additive for bituminous material modification. This study aims to evaluate the basic properties and quantify the leaching potential of modified asphalt binders incorporating crumb rubber powder (CRP) from waste tires and tin slag (TS) for a local smelting company. Three percentages of CRP and TS, at 5, 10, and 15%, were considered. The conventional asphalt binder (PEN 60/70), CRP, and TS-based modified asphalt binders were analyzed for toxicity, softening point, penetration value, elastic recovery, torsional recovery (TR), and coatability index. The findings indicated that the addition of the waste materials led to no significant heavy metal content in the asphalt binder mix. Moreover, the basic and physical properties of the asphalt binders were also improved by 5, 10, and 15% of the waste, respectively. However, TS waste exhibited limited effects on all the parameters and had a 5% optimum dosage. The modified binders’ results showed that the CRP modified asphalt binders had fewer heavy metals and responded more to elastic recovery and coatability.