A few other answers have touched on why you cannot disable individual resolutions because they are cached. If slow performance is the main issue, I have a few ideas for speeding it up. One would be to set a visible scale range to the base map. First zoom to the map scale you want (probably as far out as you'd like to see) and then you right click on the base map and "visible scale range" you can then set your minimum scale. This makes it so the basemap will only draw when zoomed in a certain amount that you set.
Additionally, this thread on geonet goes over various things to try to speed up base map rendering, its a bit outdated but some of the solutions are still applicable. One solution that looks promising is :
Open ArcCatalogue on the sidebar of your ArcMap session. Select: Add ArcGIS server then enter the url for the basemap services:
http://server.arcgisonline.com/ArcGIS/rest/services from there you can expand the menu to select the basemap you want to use and drag it into your ArcMap window. This should add the basemap to your session and render quicker.
Additionally, if you're working with projected data Arc has to work harder to convert their basemaps from
WGS_1984_Web_Mercator_Auxiliary_Sphere projection to whatever your projection is in on the fly, which can slow down load times.
I would also recommend looking into updating your graphics card or drivers to check if they're up to date. A number of people on that thread have also had luck with changing their firewall and antivirus settings to allow exceptions to ArcGIS. Such as:
.virtualearth.net (for Bing maps)
Here are some direct instructions from Esri about how to troubleshoot basemaps.