can the passenger side mirror be removed without removing the housing

Most can be removed ... you can pop most of it out (wear safety glasses) HERE is a new replacement mirror for $10.50 http://www.ebay.com/itm/1999-03-Lexus-RX300-Left-Driver-Side-Drop-Fit-Flat-Power-Door-Mirror-Glass-Lens-/291316661596?pt=Motors_Car_Truck_Parts_Accessories&fits=Year%3A1999|Make%3ALexus|Model%3ARX300&hash=item43d3d37d5c&vxp=mtr

Thank you so much for response,but I didn't get so lucky . I tried pulling it off from the bottom with a thin cloth and it would not come off. So I then looked behind the mirror to see what was going on,,and I saw two tubular ducts with torn little light blue tinicals that controls the horizontal and vertical movement . In an nut shell it looks like one unit , oh well .

No .. the mirror does come off ( or they would not make replacements).. but before you go any further make sure the mirror still adjusts ... otherwise it may have to be removed anyhow.You will need a heat gun or a good hair dryer (blower) ..after the mirror is hot .you need to get under the mirror and pry it out. Wear safety glasses because the mirror may break and emit chips